504 research outputs found
Kac-Moody Symmetric Spaces: An Addendum
No full textKac-Moody symmetric spaces have been introduced by Freyn, Hartnick, Horn and
the first-named author for centered Kac-Moody groups, that is, Kac-Moody groups
that are generated by their root subgroups. In the case of non-invertible
generalized Cartan matrices this leads to complications that -- within the
approach proposed originally -- cannot be repaired in the affine case. In the
present article we propose an alternative approach to Kac-Moody symmetric
spaces which for invertible generalized Cartan matrices provides exactly the
same concept, which for the non-affine non-invertible case provides alternative
Kac-Moody symmetric spaces, and which finally provides Kac-Moody symmetric
spaces for affine Kac-Moody groups. In a nutshell, the original intention by
Freyn, Hartnick, Horn and K\"ohl was to construct symmetric spaces that likely
lead to primitive actions of the Kac-Moody groups; this, of course, cannot work
in the affine case as affine Kac-Moody groups are far from simple
Kac–Moody symmetric spaces
No full textIn the present article we introduce and study a class of topological reflectionspaces that we call Kac–Moody symmetric spaces. These are associated with split realKac–Moody groups and generalize Riemannian symmetric spaces of noncompact split type.Based on work by the third-named author, we observe that in a non-spherical Kac–Moody symmetric space there exist pairs of points that do notlie on a common geodesic;however, any two points can be connected by a chain of geodesic segments. We moreoverclassify maximal flats in Kac–Moody symmetric spaces and study their intersection patterns,leading to a classification of global and local automorphisms. Some of our methods apply togeneral topological reflection spaces beyond the Kac–Moodysetting.Unlike Riemannian symmetric spaces, non-spherical non-affine irreducible Kac–Moodysymmetric spaces also admit an invariant causal structure.For causal and anti-causal geo-desic rays with respect to this structure we find a notion of asymptoticity, which allows usto define a future and past boundary of such Kac–Moody symmetric space. We show thatthese boundaries carry a natural polyhedral cell structureand are cellularly isomorphic togeometric realizations of the two halves of the twin buildings of the underlying split real Kac–Moody group. We also show that every automorphism of the symmetric space is uniquelydetermined by the induced cellular automorphism of the future and past boundary.The invariant causal structure on a non-spherical non-affineirreducible Kac–Moody sym-metric space gives rise to an invariant pre-order on the underlying space, and thus toa subsemigroup of the Kac–Moody group.We conclude that while in some aspects Kac–Moody symmetric spaces closely resembleRiemannian symmetric spaces, in other aspects they behave similarly tomasures, their non-Archimedean cousin
On affine Kazhdan-Lusztig R-polynomials for Kac-Moody groups
No full textIn 2019, D. Muthiah proposed a strategy to define affine Kazhdan-Lusztig R-polynomials for Kac-Moody groups. Since then, Bardy-Panse, the first author and Rousseau have introduced the formalism of twin masures and the authors have extended combinatorial results from affine root systems to general Kac-Moody root systems in a previous article. In this paper, we use these results to explicitly define affine R-Kazhdan-Lusztig polynomials for Kac-Moody groups. The construction is based on a path model lifting to twin masures. Conjecturally, these polynomials count the cardinality of intersections of opposite affine Schubert cells, as in the case of reductive groups
Epidemiologia nutricional
No full texteISBN: 978-85-7541-320-3Denise Petrucci Gigante é professora adjunta do Departamento de Nutrição e do Programa de Pós-Graduação em Epidemiologia da Universidade Federal de Pelotas.Gilberto Kac é professor adjunto do Instituto de Nutrição Josué de Castro da Universidade Federal do Rio de Janeiro.Rosely Sichieri é professora adjunta do Departamento de Epidemiologia do Instituto de Medicina Social da Universidade do Estado do Rio de Janeiro.A obra oferece uma ampla e atualizada visão dos problemas nutricionais de relevância para a saúde pública no país, tendo em vista a realidade de ensino e pesquisa e o cenário epidemiológico e nutricional atual. Publicação de fôlego e poderosa ferramenta de trabalho para a comunidade da epidemiologia nutricional, vai além da avaliação de dietas e da relação entre alimentação e doenças crônicas não transmissíveis. Valoriza, também, a longa tradição e excelência da epidemiologia brasileira no trato de temas como desnutrição, desmame precoce e carência de micronutrientes. E respeita a especificidade da dinâmica nutricional brasileira, contemplando com rigor, competência e equilíbrio métodos e análises que abrangem os ‘velhos e novos males’ da nutrição no Brasil
Universal Koszul Duality for Kac-Moody Groups
No full textWe prove a monoidal equivalence, called universal Koszul duality, between
genuine equivariant K-motives on a Kac-Moody flag variety and constructible
monodromic sheaves on its Langlands dual. The equivalence is obtained by a
Soergel-theoretic description of both sides which extends results for
finite-dimensional flag varieties by Taylor and the first author.
Universal Koszul duality bundles together a whole family of equivalences for
each point of a maximal torus. At the identity, it recovers an ungraded version
of Beilinson-Ginzburg-Soergel's and Bezrukavnikov-Yun's Koszul duality for
equivariant and unipotently monodromic sheaves. It also generalizes
Soergel-theoretic descriptions for monodromic categories on finite-dimensional
flag varieties by Lusztig-Yun, Gouttard and the second author. For affine
Kac-Moody groups, our work sheds new light on the conjectured quantum Satake
equivalences by Cautis-Kamnitzer and Gaitsgory.
On our way, we establish foundations on six functors for reduced K-motives
and introduce a formalism of constructible monodromic sheaves
Finite vs infinite decompositions in conformal embeddings
No full textBuilding on work of the first and last author, we prove that an embedding of simple affine vertex algebras , corresponding to an embedding of a maximal equal rank reductive subalgebra into a simple Lie algebra , is conformal if and only if the corresponding central charges are equal. We classify the equal rank conformal embeddings. Furthermore we describe, in almost all cases, when decomposes finitely as a -module
Influência do viés de seleção e de aferição em estimativas de tendência secular da estatura baseadas em dados da Marinha do Brasil The influence of selection and measurement bias on secular trend in height estimates from Brazilian Navy data
No full textSão apresentados dados sobre a ocorrência de viés nas estimativas de tendência secular em estatura, baseadas em dados da Marinha do Brasil. Foram analisados três bancos de dados; um para o período entre 1940 e 1965 e dois entre 1970 e 1977.Data of bias occurrence of secular height trend estimates based on Brazilian Navy data are presented. Three data sets were analyzed; one for the 1940-65 period and two for the 70s
A Realization of Certain Affine Kac-Moody Groups of Types II and III
No full textAbstractThe aim of this paper is, in the notation of Kac, to extend results about Kac-Moody algebras to corresponding groups by proving that certain affine Kac-Moody groups of types II and III arise as the fixed point subgroups of affine Kac-Moody groups of type I of higher rank under particular automorphisms. We prove an analogue of a theorem of Hée which enables us to deduce some results about the fixed point subgroups of Kac-Moody groups arising from simply-laced extended Cartan matrices under automorphisms which are the product of a graph and a diagonal automorphism. We then prove that the groups obtained in this way are in fact isomorphic to Kac-Moody groups arising from affine Cartan matrices which are not of extended type. This paper contains the main results in the author′s doctoral thesis
Lattice subgroups of Kac-Moody groups:
No full textWe utilize graphs of groups and the corresponding covering theory to study lattices in type-infinity Kac-Moody groups over a finite field of size q, including results for both cocompact and nonuniform lattices.
For every prime power q we give a sufficient condition for the rank 2 Kac-Moody group G to contain a cocompact lattice with quotient a simplex, and we show that this condition is satisfied when q is a power of 2. Under further restrictions, we show that there is an infinite descending chain of cocompact lattices, and we demonstrate such a chain for q=2. Moreover we characterize the quotient graphs of groups for each lattice. Our method involves extending coverings of edge-indexed graphs to covering morphisms of graphs of groups. We also show how this gives rise to other infinite families of cocompact lattices in G.
When q=2 we are also able to embed the infinite descending chain in the rank 3 Kac-Moody group as a chain of lattices in the subgroup generated by all non-maximal standard parabolic subgroups. In addition we embed a non-discrete subgroup in the rank 3 Kac-Moody group whose quotient is a simplex.
We next give graphs of groups descriptions for known nonuniform lattices of Nagao-type. For the nonuniform lattices SL_2 and PGL_2 over polynomial rings with base field F_q we use the theory of ramified coverings to construct the graphs of groups for their congruence subgroups. We also examine the same construction employed by Morgenstern, identifying and repairing an error in his work. All graphs of groups for non-uniform lattices constructed here satisfy the structure theorem for graphs of groups.Ph.D.Includes bibliographical references (p. 86-88)by Ila Leigh Cobb
- …
