Thesis (D. Min.)--Liberty Baptist Theological Seminary, 1999. / Includes bibliographical references.

This dissertation uses techniques from the theory of categorical actions of Kac-Moody algebras to study the analog of the BGG category O for the queer Lie superalgebra. Chen recently reduced many questions about this category to its so-called types A, B, and C blocks. The type A blocks were completely described in joint work with Brundan in terms of the general linear Lie superalgebra. This dissertation proves that the type C blocks admit the structure of a tensor product categorification of the n-fold tensor power of the natural sp_\infty-module. Using this result, we relate the combinatorics for these blocks to Webster’s orthodox bases for the quantum group of type C_\infty, verifying the truth of a recent conjecture of Cheng-Kwon-Wang. This dissertation contains coauthored material.

Orientador: Marcio Antonio de Faria Rosa / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Fisica "Gleb Wataghin" / Made available in DSpace on 2018-07-21T14:47:17Z (GMT). No. of bitstreams: 1 Shimabukuro_AlexItiro_M.pdf: 4437200 bytes, checksum: 1542cdddcbae2d5fa2e25f10ffa05fb5 (MD5) Previous issue date: 1995 / Resumo: Não informado / Abstract: Not informed. / Mestrado / Física / Mestre em Física

In this thesis, we extend the construction of the formal (affine) Demazure algebra due to Hoffnung, Malagón-López, Savage and Zainoulline in two directions. First, we introduce and study the notion of formal Demazure lattices of a Kac-Moody root system and show that the definitions and properties of the formal (affine) Demazure operators and algebras hold for such lattices. Second, we show that for the hyperbolic formal group law the formal Demazure algebra is isomorphic (after extending the coefficients) to the Hecke algebra.

No description available.

Este trabalho tem como objetivo principal estudar módulos irredutíveis sobre as álgebras de Kac-Moody afim, conforme [7]. Em particular, a técnica de localização foi aplicada aos módulos de Verma imaginários sobre a álgebra de Lie afim A(1)1, com o objetivo de obter novos módulos irredutíveis sobre essa álgebra. Conforme [8] e [6], é o mesmo que aplicar a técnica de localização à primeira realização de campos livres de A(1)1 .Para cumprir o objetivo, introduzimos as álgebras de Kac-Moody, tendo como foco principal as álgebras de Kac-Moody do tipo afim, conforme [14]. Em seguida, definimos os módulos de Verma,destacando os módulos de Verma imaginários sobre a álgebra de Lie afim A(1)1, conforme [8]. / The main purpose of this work is to study the irreducible modules of affine Kac-Moody algebras,according to [7].In particular, the localization technique was applied to the imaginary Verma modules of affine Lie algebra A(1)1, with the purpose to obtain new irreducible modules of this algebra. According to[8] and [6], it is the same as to apply the localization technique to the first realization of free fields of A(1)1.To achieve the purpose, we introduced the Kac-Moody algebras, having the main focus the af-fine Kac-Moody algebras, according to [14]. Following, we defined the Verma modules, highlighting imaginary Verma modules of affine Lie algebra A(1)1, according to [8].

Parmi les représentations linéaires des groupes de tresses, les représentations de Burau peuvent être construites à partir d’une représentation triviale via une construction introduite par Long en 1994, à l’issue d’une collaboration avec Moody. Cette construction, dite de Long-Moody, permet ainsi de construire des représentations de plus en plus complexes des groupes de tresses. Dans cette thèse, on adopte un point de vue fonctoriel sur cette construction, ce qui permet d’en dégager plus aisément des variantes. De plus, le degré de polynomialité d’un foncteur permet d’en mesurer la complexité. On montre ainsi que la construction Long-Moody définit un foncteur LM, qui augmente le degré de très forte polynomialité. Par ailleurs, on définit des foncteurs analogues pour d’autres familles de groupes telles que les groupes de difféotopie des surfaces et des 3-variétés, les groupes symétriques ou les groupes d’automorphismes des groupes libres. Ils vérifient des propriétés similaires sur la polynomialité. Les foncteurs de Long-Moody fournissent ainsi des coefficients tordus entrant dans le cadre des résultats de stabilité homologique de Randal-Williams et Wahl pour les familles de groupes susmentionnées. On donne enfin un résultat de comparaison entre l’homologie stable à coefficient dans un foncteur F et celle à coefficient dans le foncteur LM(F) obtenu en appliquant un foncteur de Long-Moody. Cette thèse se décompose en trois chapitres. Le premier introduit les foncteurs de Long-Moody pour les groupes de tresses et traite de leur effet sur la polynomialité. Le deuxième traite de la généralisation des foncteurs de Long-Moody pour d’autres familles de groupes. Le dernier chapitre concerne des calculs d’homologie stable pour les groupes de difféotopie. / Among the linear representations of braid groups, Burau representations are recovered from a trivial representation using a construction introduced by Long in 1994, following a collaboration with Moody. This construction, called the Long-Moody construction, thus allows to construct more and more complex representations of braid groups. In this thesis, we have a functorial point of view on this construction, which allows find more easily some variants. Moreover, the degree of polynomiality of a functor measures its complexity. We thus show that the Long-Moody construction defines a functor LM, which increases the degree of polynomiality. Furthermore, we define analogous functors for other families of groups such as mapping class groups of surfaces and 3-manifolds, symmetric groups or automorphism groups of free groups. They satisfy similar properties on the polynomiality. Hence, Long-Moody functors provide twisted coefficients fitting into the framework of the homological stability results of Randal-Williams and Wahl for the afore mentioned families of groups. Finally, we give a comparison result for the stable homology with coefficient given by a functor F and the one with coefficient given by the functor LM(F), obtained applying a Long-Moody functor. This thesis has three chapters. The first one introduces Long-Moody functors for braid groups and deals with their effect on the polynomiality. The first one deals with the generalisation of Long-Moody functors for other families of groups. The last chapter touches on stable homology computations for mapping class group.

Este trabalho tem como objetivo principal estudar módulos irredutíveis sobre as álgebras de Kac-Moody afim, conforme [7]. Em particular, a técnica de localização foi aplicada aos módulos de Verma imaginários sobre a álgebra de Lie afim A(1)1, com o objetivo de obter novos módulos irredutíveis sobre essa álgebra. Conforme [8] e [6], é o mesmo que aplicar a técnica de localização à primeira realização de campos livres de A(1)1 .Para cumprir o objetivo, introduzimos as álgebras de Kac-Moody, tendo como foco principal as álgebras de Kac-Moody do tipo afim, conforme [14]. Em seguida, definimos os módulos de Verma,destacando os módulos de Verma imaginários sobre a álgebra de Lie afim A(1)1, conforme [8]. / The main purpose of this work is to study the irreducible modules of affine Kac-Moody algebras,according to [7].In particular, the localization technique was applied to the imaginary Verma modules of affine Lie algebra A(1)1, with the purpose to obtain new irreducible modules of this algebra. According to[8] and [6], it is the same as to apply the localization technique to the first realization of free fields of A(1)1.To achieve the purpose, we introduced the Kac-Moody algebras, having the main focus the af-fine Kac-Moody algebras, according to [14]. Following, we defined the Verma modules, highlighting imaginary Verma modules of affine Lie algebra A(1)1, according to [8].

L’œuvre de Rick Moody échappe à toute tentative de catégorisation générique, elle est à la croisée de styles qui s’entrechoquent et se heurtent pour donner naissance à une prose hétéroclite. Cette fiction protéiforme n’en demeure pas moins traversée par la répétition d’un motif invariant : l’accident. C’est le paradoxe de cette observation qui constitue le point de départ de cette thèse. Comment l’accident, dont le surgissement paraît toujours fulgurant, instantané et unique, peut-il se voir répété, décliné et transformé en un principe structurant qui préside à la composition de l’oeuvre de Rick Moody ? Pour répondre à cette question, il faut nécessairement changer le présupposé sur lequel repose la définition de l’accident pour qu’il ne soit plus seulement envisagé comme ce qui arrive de manière accidentelle mais pour que soit révélée également sa dimension essentielle. Cela revient à proposer l’hypothèse que l’accident est toujours déjà là, qu’il est ontologique. Ce changement de perspective, rendu possible par une manipulation temporelle, encourage, sur le plan de l’analyse littéraire, une étude de la temporalité de l’accident. Son surgissement induit plus largement la question de la représentation de la réalité tandis que sa répétition autorise son inscription dans une durée. Provoquant toujours une rupture, la temporalité de l’accident est double car elle a la possibilité à la fois de mettre un terme et de faire éclore un nouveau début. L’accident crée des formes et des cycles, il surgit, dure, détruit, mais aussi régénère. / The books of Rick Moody evade all possibility for a generic categorization. They standat the crossroads of different styles which collide with one another and give birth to a heterogeneous prose. However, at the heart of Moody’s protean fiction is to be found a recurring motif : the accident. The repetition of this pattern and the paradox it arises are what started this dissertation. How can such a motif be repeated and transformed into an unvarying organization principle since, at its core, the accident is supposed to happen in a flash, only once? The answer to this question lies in a change of perspective. The definition of the accident needs to be challenged so that it allows for the possibility to consider it not only as what happens accidentally but what is bound to happen by necessity. It all amounts to suggesting that the accident is ontological ; it is always already present, on the verge of happening. This temporal shift makes it necessary, in aliterary perspective, to analyze the temporality of the accident. The sudden appearance of the accident raises questions about the strategies fiction has at its disposal torepresent reality. The repetition of the accident induces also a reflection on its duration.The break-up it necessarily generates reveals its dual temporality: it either comes as an ending or as a possibility for a new beginning. The accident creates different shapes, forms and cycles as it comes up, destroys and regenerates.

Orientador: Adriano Adrega de Moura / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-08-15T13:08:41Z (GMT). No. of bitstreams: 1 Pereira_FernandadeAndrade_M.pdf: 1042187 bytes, checksum: adcbcf9ff1fb8219267fb3097af14c9d (MD5) Previous issue date: 2010 / Resumo: O conceito de afinização minimal, introduzido por V. Chari e A. Pressley, surgiu a partir da impossibilidade de se estender, em geral, uma representação do grupo quântico associado a uma álgebra de Lie simples para o grupo quântico associado à sua álgebra de laços, o que sempre é possível no contexto clássico. Uma classe especial de afinizações minimais é a dos módulos de Kirillov-Reshetikhin, que são afinizações minimais dos módulos irredutíveis quando os pesos máximos são múltiplos dos pesos fundamentais. Esses módulos são objetos de muitos estudos por causa das suas aplicações em física-matemática. Um problema de interesse particular envolvendo afinizações minimais é o de descrever seus caracteres. Neste trabalho apresentamos algumas fórmulas para os caracteres de afinizações minimais quando a álgebra de Lie simples envolvida é do tipo E6. A principal técnica utilizada foi proposta por V. Chari e A. Moura ao se considerar o limite clássico das afinizações minimais. As fórmulas são obtidas através de um estudo sistemático de certos módulos graduados dados por geradores e relações para a correspodente álgebra de correntes. O ponto principal é demonstrar que estes módulos são isomorfos aos limites clássicos das afinizações minimais quando vistos como módulos para a álgebra de correntes / Abstract: The concept of minimal affinization, introduced by V. Chari and A. Pressley, arose from the impossibility of extending, in general, a representation of the quantum group associated to a simple Lie algebra to the quantum group associated to its loop algebra, which is always possible on the classical context. A special class of minimal affinizations is that of Kirillov-Reshetikhin modules, which are minimal affinizations of the irreducible modules having multiples of the fundamental weights as highest weights. These modules are objects of intensive studies because of their applications in mathematical physics. One problem of particular interest involving minimal affinizations is that of describing their characters. In this work we present some formulas for the characters of minimal affinizations when the simple Lie algebra involved is of type E6. The main strategy used here was proposed by V. Chari and A. Moura by considering the classical limit of minimal affinizations. The formulas are obtained through a systematic study of certain graded modules for the corresponding current algebra given by generators and relations. The main point is to prove that these modules are isomorphic to the classical limits of the minimal affinizations when the latter are regarded as modules for the current algebra / Mestrado / Algebra / Mestre em Matemática