96 research outputs found
Indigenous Peoples and Litigation:Strategies for Legal Empowerment
No full textAcross the globe indigenous peoples are increasingly using litigation to seek remedies for violation of their fundamental human rights. The rise of litigation is to be placed in the larger issue of increased land grabbing, natural resources exploitation and the general lack of recognition of their rights at the national level. This lack of legal rights is usually coupled with a lack of political will to address the issues faced by indigenous peoples, often leading to serious human rights violations, leaving indigenous advocates with few options but to turn to courts as a last resort to seek remedies. This article examines some of the issues faced by indigenous peoples and their advocates when engaging in human rights litigation. The goal is to offer a practice-based reflection on the encounter between courts and indigenous peoples with a specific focus on analysing strategies to ensure their legal empowerment. This is particularly important knowing the technicality, externalities and complexities of the process of litigation, and the fact that many decisions do not get implemented. In this context this article explores how the process of litigation in itself can support legal empowerment and the wider fight for justice. © 2020, The Author(s). The attached document (embargoed until 10/10/2022) is an author produced version of a paper published in JOURNAL OF HUMAN RIGHTS PRACTICE uploaded in accordance with the publisher’s self-archiving policy. The final published version (version of record) is available online at the link. Some minor differences between this version and the final published version may remain. We suggest you refer to the final published version should you wish to cite from it.<br/
Some computations about Kazhdan-Lusztig cells in affine Weyl groups of rank 2
No full textIn the last section of the paper "Generalized induction of Kazhdan-Lusztig cells" and in "Kazhdan-Lusztig cells in affine Weyl groups of rank 2" the author described the partition into Kazhdan-Lusztig cells of the affine Weyl groups of rank 2 for all choices of parameters. The proof of these results relies on some explicit computations with GAP. In these notes we give some details of these computations
Ordering Families using Lusztig's symbols in type B: the integer case
No full text23 pages, 11 figuresLet \Irr(W) be the set of irreducible representations of a finite Weyl group . Following an idea from Spaltenstein, Geck has recently introduced a preorder on \Irr(W) in connection with the notion of Lusztig families. In a later paper with Iancu, they have shown that in type (in the asymptotic case and in the equal parameter case) this order coincides with the order on Lusztig symbols as defined by Geck and the second author in \cite{GJ}. In this paper, we show that this caracterisation extends to the so-called integer case, that is when the ratio of the parameters is an integer
Cellules de Kazhdan-Lusztig dans les groupes de Weyl affines à paramètres inégaux
No full textHecke algebras arise naturally in the representation theory of reductive groups over finite or p-adic fields. These algebras are specializations of Iwahori-Hecke algebras which can be defined in terms of a Coxeter group and a weight function without reference to reductive groups and this is the setting we are working in. Kazhdan-Lusztig cells play a crucial role in the study of Iwahori-Hecke algebras. The aim of this work is to study the Kazhdan-Lusztig cells in affine Weyl groups with unequal parameters. More precisely, we show that the Kazhdan-Lusztig polynomials of an affine Weyl group are invariant under ``long enough'' translations, we decompose the lowest two-sided cell into left cells and we determine the decomposition of the affine Weyl group of type G into cells for a whole class of weight functions.Les algèbres de Hecke apparaissent naturellement dans la théorie des représentations des groupes réductifs sur des corps finis ou p-adiques. Ces algèbres sont des spécialisations des algèbres de Iwahori-Hecke qui peuvent être définies de manière combinatoire à partir d'un groupe de Coxeter et d'une fonction de poids sans faire référence à la théorie des groupes réductifs. C'est ce point de vue qui est adopté dans ce travail. Les cellules de Kazhdan-Lusztig jouent un rôle fondamental dans l'étude des algèbres de Iwahori-Hecke. Le but de ce travail est d'étudier les cellules de Kazhdan-Lusztig dans les groupes de Weyl affines à paramètres inégaux. Les principaux résultats de cette thèse sont l'invariance des polynômes de Kazhdan-Lusztig par translation, la décomposition de la cellule bilatère minimale en cellules gauches et la décomposition du groupe de Weyl affine de type G en cellules pour toute une classe de fonctions de poids
On the determination of Kazhdan-Lusztig cells in affine Weyl groups with unequal parameters
No full textInternational audienceLet W be a Coxeter group and L be a weight function on W. Following Lusztig, we have a corresponding decomposition of W into left cells, which have important applications in representation theory. We study the case where W is an affine Weyl group of type G2~. Using explicit computation with \textsf{CHEVIE}, we show that (1) there are only finitely many possible decompositions into left cells and (2) the number of left cells is finite in each case, thus confirming some of Lusztig's conjectures in this case. For the proof, we show some equalities on the Kazhdan-Lusztig polynomials which hold for any affine Weyl groups
Cellules de Kazhdan-Lusztig dans les groupes de Weyl affines à paramètres inégaux
No full textHecke algebras arise naturally in the representation theory of reductive groups over finite or p-adic fields. These algebras are specializations of Iwahori-Hecke algebras which can be defined in terms of a Coxeter group and a weight function without reference to reductive groups and this is the setting we are working in. Kazhdan-Lusztig cells play a crucial role in the study of Iwahori-Hecke algebras. The aim of this work is to study the Kazhdan-Lusztig cells in affine Weyl groups with unequal parameters. More precisely, we show that the Kazhdan-Lusztig polynomials of an affine Weyl group are invariant under ``long enough'' translations, we decompose the lowest two-sided cell into left cells and we determine the decomposition of the affine Weyl group of type G into cells for a whole class of weight functions.Les algèbres de Hecke apparaissent naturellement dans la théorie des représentations des groupes réductifs sur des corps finis ou p-adiques. Ces algèbres sont des spécialisations des algèbres de Iwahori-Hecke qui peuvent être définies de manière combinatoire à partir d'un groupe de Coxeter et d'une fonction de poids sans faire référence à la théorie des groupes réductifs. C'est ce point de vue qui est adopté dans ce travail. Les cellules de Kazhdan-Lusztig jouent un rôle fondamental dans l'étude des algèbres de Iwahori-Hecke. Le but de ce travail est d'étudier les cellules de Kazhdan-Lusztig dans les groupes de Weyl affines à paramètres inégaux. Les principaux résultats de cette thèse sont l'invariance des polynômes de Kazhdan-Lusztig par translation, la décomposition de la cellule bilatère minimale en cellules gauches et la décomposition du groupe de Weyl affine de type G en cellules pour toute une classe de fonctions de poids
Cellularity of the lowest two-sided ideal of an affine Hecke algebra
No full text26 pages, 6 figuresIn this paper we show that the lowest two-sided ideal of an affine Hecke algebra is affine cellular for all choices of parameters. We explicitely describe the cellular basis and we show that the basis elements have a nice decomposition when expressed in the Kazhdan-Lusztig basis. In type we provide a combinatorial description of this decomposition in term of number of paths
Cellularity of the lowest two-sided ideal of an affine Hecke algebra
No full text26 pages, 6 figuresIn this paper we show that the lowest two-sided ideal of an affine Hecke algebra is affine cellular for all choices of parameters. We explicitely describe the cellular basis and we show that the basis elements have a nice decomposition when expressed in the Kazhdan-Lusztig basis. In type we provide a combinatorial description of this decomposition in term of number of paths
Cellules de Kazhdan-Lusztig dans les groupes de Weyl affines à paramètres inégaux
No full textHecke algebras arise naturally in the representation theory of reductive groups over finite or p-adic fields. These algebras are specializations of Iwahori-Hecke algebras which can be defined in terms of a Coxeter group and a weight function without reference to reductive groups and this is the setting we are working in. Kazhdan-Lusztig cells play a crucial role in the study of Iwahori-Hecke algebras. The aim of this work is to study the Kazhdan-Lusztig cells in affine Weyl groups with unequal parameters. More precisely, we show that the Kazhdan-Lusztig polynomials of an affine Weyl group are invariant under ``long enough'' translations, we decompose the lowest two-sided cell into left cells and we determine the decomposition of the affine Weyl group of type G into cells for a whole class of weight functions.Les algèbres de Hecke apparaissent naturellement dans la théorie des représentations des groupes réductifs sur des corps finis ou p-adiques. Ces algèbres sont des spécialisations des algèbres de Iwahori-Hecke qui peuvent être définies de manière combinatoire à partir d'un groupe de Coxeter et d'une fonction de poids sans faire référence à la théorie des groupes réductifs. C'est ce point de vue qui est adopté dans ce travail. Les cellules de Kazhdan-Lusztig jouent un rôle fondamental dans l'étude des algèbres de Iwahori-Hecke. Le but de ce travail est d'étudier les cellules de Kazhdan-Lusztig dans les groupes de Weyl affines à paramètres inégaux. Les principaux résultats de cette thèse sont l'invariance des polynômes de Kazhdan-Lusztig par translation, la décomposition de la cellule bilatère minimale en cellules gauches et la décomposition du groupe de Weyl affine de type G en cellules pour toute une classe de fonctions de poids
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