31 research outputs found
Recycling citizenship: infrastructural transformation and access struggles in Dakar's solid waste management system
Get PDFIn transforming the city's waste infrastructure towards mechanized incineration, a pending waste management reform in Dakar stands to dispossess over a thousand recycling workers, whose future access to waste and participation in the city's waste system is in limbo. In the face of an infrastructural reform that compromises their livelihoods, the workers draw on their ties to global civil society actors and a transnational advocacy network as they mobilize to defend their access to waste. This study analyzes the workers’ mobilization as a citizenship struggle, given that their claims signify efforts to influence the political economy that shapes their livelihoods. Situated at the intersection of infrastructural violence, transnational activism, and substantive citizenship scholarship, this research draws on qualitative field research and document analysis to show how ties to global civil society actors can erode the practice of citizenship by weakening the capacity of the workers to be politically engaged and to shape the fate of their polity. In this case, the international civil society groups and transnational advocacy networks involved are financially supportive but politically uninvolved in ways that distance the workers from the state and disenable them from influencing government decision making. The emphasis in transnational activism literature on the emancipatory implications of local-global alliances for local struggles thus needs to be further scrutinized with respect to the ways in which these alliances transform local practices and formulations of citizenship.Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2018-05-01The student, Rea Zaimi, accepted the attached license on 2015-11-19 at 14:54.The student, Rea Zaimi, submitted this Thesis for approval on 2015-11-19 at 15:01.This Thesis was approved for publication on 2015-12-01 at 16:49.DSpace SAF Submission Ingestion Package generated from Vireo submission #8809 on 2016-07-07 at 13:48:01Made available in DSpace on 2016-07-07T20:26:35Z (GMT). No. of bitstreams: 2
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Algèbre d'Askey–Wilson, centralisateurs et fonctions spéciales (bi)orthogonales
Get PDFCette thèse est divisée en quatre parties qui portent sur les centralisateurs des algèbres quantiques , les polynômes biorthogonaux avec propriétés bispectrales, les polynômes bivariés de Griffiths, et les schémas d'association avec structures polynomiales bivariées. Le fil conducteur principal entre ces parties est l'algèbre d'Askey–Wilson.
Dans la première partie, l'idée principale est de combiner l'algèbre du groupe des tresses avec l'algèbre d'Askey–Wilson dans des situations qui impliquent les centralisateurs de . Ainsi, on obtient des représentations du groupe des tresses en termes de polynômes orthogonaux de -Racah par le biais de matrices de , on obtient une interprétation de l'algèbre d'Askey–Wilson dans le cadre de la théorie topologique des champs de Chern–Simons avec groupe de jauge ainsi que dans le cadre des invariants d'entrelacs associés à , et on offre une description algébrique complète du centralisateur de dans un produit tensoriel de trois représentations irréductibles identiques de spin quelconque. Dans une optique différente, on offre aussi une présentation algébrique de certaines algèbres de Hecke fusionnées qui décrivent des centralisateurs de .
Dans la deuxième partie, on étudie deux familles de polynômes biorthogonaux par des méthodes algébriques, offrant une extension du tableau qui existe pour les polynômes orthogonaux classiques de type Askey–Wilson. Les deux familles considérées sont les polynômes de type Hahn et les polynômes de Pastro. Dans les deux cas, l'idée est d'introduire un triplet d'opérateurs ayant une action tridiagonale et d'obtenir les polynômes comme solutions à deux problèmes aux valeurs propres généralisés provenant de ce triplet. On trouve les propriétés de bispectralité et de biorthogonalité des polynômes en se servant des opérateurs du triplet, et on détermine l'algèbre réalisée par les opérateurs.
Dans la troisième partie, on caractérise deux familles de polynômes bivariés de Griffiths. La première famille est une généralisation des polynômes de Griffiths de type Krawtchouk qui dépend d'un paramètre . On trouve leurs relations de bispectralité et leur biorthogonalité en utilisant les propriétés des polynômes de Krawtchouk à une variable. Les relations de contiguïté des polynômes univariés jouent un rôle essentiel dans les calculs. On utilise des méthodes semblables pour caractériser la deuxième famille, qui est formée de polynômes de Griffiths de type Racah. Ceux-ci sont orthogonaux.
Dans la quatrième partie, on propose une généralisation bivariée des propriétés - et -polynomiales pour les schémas d'association et de concepts reliés. Plusieurs exemples de schémas vérifiant la propriété -polynomiale bivariée sont obtenus. On montre que les schémas de Johnson non-binaires ainsi que leurs analogues -déformés, les schémas définis à partir d'espaces atténués, sont - et -polynomiaux bivariés en étudiant les propriétés bispectrales des polynômes bivariés associés. Les structures algébriques reliées à ces schémas sont explorées. On propose aussi une généralisation multivariée des graphes distance-réguliers, et on montre que ceux-ci sont en correspondance avec des schémas -polynomiaux multivariés. Finalement, on étudie une sous-classe de paires de Leonard de rang 2 qui font intervenir des polynômes bivariés factorisés.This thesis is divided in four parts concerning centralizers of quantum algebras ,
biorthogonal polynomials with bispectral properties, bivariate Griffiths polynomials, and association schemes with bivariate polynomial structures. The main topic relating all these parts is the Askey–Wilson algebra.
In the first part, the main idea is to combine the braid group algebra with the Askey–Wilson algebra in situations involving the centralizers of the quantum algebra . Hence, we obtain representations of the braid group in terms of -Racah orthogonal polynomials using -matrices of , we obtain an interpretation of the Askey–Wilson algebra in the framework of Chern–Simons topological quantum field theory with gauge field as well as in the framework of link invariants associated to , and we provide a complete algebraic description of the centralizer of in the tensor product of three identical irreducible representations of any spin. In a different perspective, we also provide an algebraic presentation of some fused Hecke algebras, which describe some centralizers of .
In the second part, we study two families of biorthogonal polynomials using algebraic methods, hence extending the picture that exists for the classical orthogonal polynomials of the Askey–Wilson type. The two families that we consider are the polynomials of Hahn type and the Pastro polynomials. In both cases, the idea is to introduce a triplet of operators with tridiagonal actions and obtain the polynomials as solutions of two generalized eigenvalue problems involving this triplet. We find the bispectrality and biorthogonality properties of the polynomials using the operators of the triplet, and we determine the algebra realized by the operators.
In the third part, we characterize two families of bivariate Griffiths polynomials. The first family is a generalization of the Griffiths polynomials of Krawtchouk type which depends on a parameter . We find their bispectrality relations and their biorthogonality by using the properties of univariate Krawtchouk polynomials. The contiguity relations of the univariate polynomials play a key role in the computations. We use similar methods to characterize the second family, which is formed by Griffiths polynomials of Racah type. These are orthogonal.
In the fourth part, we propose a bivariate generalization of the - and -polynomial properties of association schemes and related concepts. Several examples of schemes satisfying the bivariate -polynomial property are obtained. We show that the non-binary Johnson schemes and their -deformed analogs, the schemes based on attenuated spaces, are bivariate - and -polynomial by studying the bispectral properties of the associated bivariate polynomials. The algebraic structures related to these schemes are explored. We also propose a multivariate generalization of distance-regular graphs, and we show that these are in correspondence with multivariate -polynomial schemes. Finally, we study a subclass of rank 2 Leonard pairs involving factorized bivariate polynomials
Algèbres de Temperley-Lieb, Birman-Murakami-Wenzl et Askey-Wilson, et autres centralisateurs de U_q(sl_2)
Get PDFMémoire par articles.Ce mémoire contient trois articles reliés par l'idée sous-jacente d'une généralisation de la dualité de Schur-Weyl. L'objectif principal est d'obtenir une description algébrique du centralisateur de l'image de l'action diagonale de U_q(sl_2) dans le produit tensoriel de trois représentations irréductibles, lorsque q n'est pas une racine de l'unité. La relation entre une algèbre de Askey-Wilson étendue AW(3) et ce centralisateur est examinée à cet effet. Dans le premier article, les éléments du centralisateur de l'action de U_q(sl_2) dans son produit tensoriel triple sont définis à l'aide de la matrice R universelle de U_q(sl_2). Il est montré que ces éléments respectent les relations définissantes de AW(3). Dans le deuxième article, la matrice R universelle de la superalgèbre de Lie osp(1|2) est utilisée de manière similaire avec l'algèbre de Bannai-Ito BI(3). Dans ce cas, le formalisme de la matrice R permet de définir l'algèbre de Bannai-Ito de rang supérieur BI(n) comme le centralisateur de l'action de osp(1|2) dans son produit tensoriel n-fois. Le troisième article propose une conjecture qui établit un isomorphisme entre un quotient de AW(3) et le centralisateur de l'image de l'action diagonale de U_q(sl_2) dans le produit tensoriel de trois représentations irréductibles quelconques. La conjecture est prouvée pour plusieurs cas, et les algèbres de Temperley-Lieb, Birman-Murakami-Wenzl et Temperley-Lieb à une frontière sont retrouvées comme quotients de l'algèbre de Askey-Wilson.This master thesis contains three articles related by the underlying idea of a generalization of the Schur-Weyl duality. The main objective is to obtain an algebraic description of the centralizer of the image of the diagonal action of U_q(sl_2) in the tensor product of three irreducible representations, when q is not a root of unity. The connection between a centrally extended Askey-Wilson algebra AW(3) and this centralizer is examined for this purpose. In the first article, the elements of the centralizer of the action of U_q(sl_2) in its threefold tensor product are defined with the help of the universal R-matrix of U_q(sl_2). These elements are shown to satisfy the defining relations of AW(3). In the second article, the universal R-matrix of the Lie superalgebra osp(1|2) is used in a similar fashion with the Bannai-Ito algebra BI(3). In this case, the formalism of the R-matrix allows to define the higher rank Bannai-Ito algebra BI(n) as the centralizer of the action of osp(1|2) in its n-fold tensor product. The third article proposes a conjecture that establishes an isomorphism between a quotient of AW(3) and the centralizer of the image of the diagonal action of U_q(sl_2) in the tensor product of any three irreducible representations. The conjecture is proved for several cases, and the Temperley-Lieb, Birman-Murakami-Wenzl and one-boundary Temperley-Lieb algebras are recovered as quotients of the Askey-Wilson algebra
Bannai–Ito algebras and the universal R-matrix of osp(1|2)
No full text10 pages, 15 ref.International audienceThe Bannai-Ito algebra BI(n) is viewed as the centralizer of the action of osp(1|2) in the n-fold tensor product of the universal algebra of this Lie superalgebra. The generators of this centralizer are constructed with the help of the universal R-matrix of osp(1|2). The specific structure of the osp(1|2) embeddings to which the centralizing elements are attached as Casimir elements is explained. With the generators defined, the structure relations of BI(n) are derived from those of BI(3) by repeated action of the coproduct and using properties of the R-matrix and of the generators of the symmetric group Sn
Temperley–Lieb, Birman–Murakami–Wenzl and Askey–Wilson Algebras and Other Centralizers of
No full textInternational audienceThe centralizer of the image of the diagonal embedding of in the tensor product of three irreducible representations is examined in a Schur–Weyl duality spirit. The aim is to offer a description in terms of generators and relations. A conjecture in this respect is offered with the centralizers presented as quotients of the Askey–Wilson algebra. Support for the conjecture is provided by an examination of the representations of the quotients. The conjecture is also shown to be true in a number of cases thereby exhibiting in particular the Temperley–Lieb, Birman–Murakami–Wenzl and one-boundary Temperley–Lieb algebras as quotients of the Askey–Wilson algebra
Factorized -Leonard pair
Get PDFThe notion of factorized -Leonard pair is introduced. It is defined as a
rank 2 Leonard pair, with actions in certain bases corresponding to the root
system of the Weyl group , and with some additional properties. The
functions arising as entries of transition matrices are bivariate orthogonal
polynomials (of Tratnik type) with bispectral properties. Examples of
factorized -Leonard pairs are constructed using classical Leonard pairs
associated to families of orthogonal polynomials of the (-)Askey scheme. The
most general examples are associated to an intricate product of univariate
(-)Hahn and dual (-)Hahn polynomials.Comment: 33 page
Factorized -Leonard pair
No full text33 pagesInternational audienceThe notion of factorized -Leonard pair is introduced. It is defined as a rank 2 Leonard pair, with actions in certain bases corresponding to the root system of the Weyl group , and with some additional properties. The functions arising as entries of transition matrices are bivariate orthogonal polynomials (of Tratnik type) with bispectral properties. Examples of factorized -Leonard pairs are constructed using classical Leonard pairs associated to families of orthogonal polynomials of the (-)Askey scheme. The most general examples are associated to an intricate product of univariate (-)Hahn and dual (-)Hahn polynomials
Revisiting the Askey–Wilson algebra with the universal R -matrix of Uq(su(2))
No full textInternational audienceA description of the embedding of a centrally extended Askey–Wilson algebra, AW(3), in Uq(sl2) 3 is given in terms of the universal R-matrix of Uq(sl2). The generators of the centralizer of Uq(sl2) in its three-fold tensor product are naturally expressed through conjugations of Casimir elements with R. They are seen as the images of the generators of AW(3) under the embedding map by showing that they obey the AW(3) relations. This is achieved by introducing a natural coaction also constructed with the help of the R-matrix
A bivariate Q-polynomial structure for the non-binary Johnson scheme
No full textInternational audienceThe notion of multivariate -and -polynomial association scheme has been introduced recently, generalizing the well-known univariate case. Numerous examples of such association schemes have already been exhibited. In particular, it has been demonstrated that the non-binary Johnson scheme is a bivariate -polynomial association scheme. We show here that it is also a bivariate -polynomial association scheme for some parameters. This provides, with the -polynomial structure, the bispectral property (i.e. the recurrence and difference relations) of a family of bivariate orthogonal polynomials made out of univariate Krawtchouk and dual Hahn polynomials. The algebra based on the bispectral operators is also studied together with the subconstituent algebra of this association scheme
BRAID GROUP AND q-RACAH POLYNOMIALS
No full textInternational audienceThe irreducible representations of two intermediate Casimir elements associated to the recoupling of three identical irreducible representations of U q (sl 2) are considered. It is shown that these intermediate Casimirs are related by a conjugation involving braid group representations. Consequently, the entries of the braid group matrices are explicitly given in terms of the q-Racah polynomials which appear as 6j-symbols in the Racah problem for U q (sl 2). Formulas for these polynomials are derived from the algebraic relations satisfied by the braid group representations
