Cohomology For Quantum Groups Via The Geometry Of The Nullcone

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Cohomology For Quantum Groups Via The Geometry Of The Nullcone

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Author : Christopher P. Bendel
language : en
Publisher: American Mathematical Soc.
Release Date : 2014-04-07

Cohomology For Quantum Groups Via The Geometry Of The Nullcone written by Christopher P. Bendel and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-04-07 with Mathematics categories.

In general, little is known about the representation theory of quantum groups (resp., algebraic groups) when l (resp., p ) is smaller than the Coxeter number h of the underlying root system. For example, Lusztig's conjecture concerning the characters of the rational irreducible G -modules stipulates that p=h. The main result in this paper provides a surprisingly uniform answer for the cohomology algebra H (u ? ,C) of the small quantum group.

Categorical Combinatorial And Geometric Representation Theory And Related Topics

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Author : Pramod N. Achar
language : en
Publisher: American Mathematical Society
Release Date : 2024-07-11

Categorical Combinatorial And Geometric Representation Theory And Related Topics written by Pramod N. Achar and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-07-11 with Mathematics categories.

This book is the third Proceedings of the Southeastern Lie Theory Workshop Series covering years 2015–21. During this time five workshops on different aspects of Lie theory were held at North Carolina State University in October 2015; University of Virginia in May 2016; University of Georgia in June 2018; Louisiana State University in May 2019; and College of Charleston in October 2021. Some of the articles by experts in the field describe recent developments while others include new results in categorical, combinatorial, and geometric representation theory of algebraic groups, Lie (super) algebras, and quantum groups, as well as on some related topics. The survey articles will be beneficial to junior researchers. This book will be useful to any researcher working in Lie theory and related areas.

Geometric And Topological Aspects Of The Representation Theory Of Finite Groups

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Author : Jon F. Carlson
language : en
Publisher: Springer
Release Date : 2018-10-04

Geometric And Topological Aspects Of The Representation Theory Of Finite Groups written by Jon F. Carlson and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-04 with Mathematics categories.

These proceedings comprise two workshops celebrating the accomplishments of David J. Benson on the occasion of his sixtieth birthday. The papers presented at the meetings were representative of the many mathematical subjects he has worked on, with an emphasis on group prepresentations and cohomology. The first workshop was titled "Groups, Representations, and Cohomology" and held from June 22 to June 27, 2015 at Sabhal Mòr Ostaig on the Isle of Skye, Scotland. The second was a combination of a summer school and workshop on the subject of "Geometric Methods in the Representation Theory of Finite Groups" and took place at the Pacific Institute for the Mathematical Sciences at the University of British Columbia in Vancouver from July 27 to August 5, 2016. The contents of the volume include a composite of both summer school material and workshop-derived survey articles on geometric and topological aspects of the representation theory of finite groups. The mission of the annually sponsored Summer Schools is to train and draw new students, and help Ph.D students transition to independent research.

A Geometric Theory For Hypergraph Matching

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Author : Peter Keevash
language : en
Publisher: American Mathematical Soc.
Release Date : 2014-12-20

A Geometric Theory For Hypergraph Matching written by Peter Keevash and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-12-20 with Mathematics categories.

The authors develop a theory for the existence of perfect matchings in hypergraphs under quite general conditions. Informally speaking, the obstructions to perfect matchings are geometric, and are of two distinct types: `space barriers' from convex geometry, and `divisibility barriers' from arithmetic lattice-based constructions. To formulate precise results, they introduce the setting of simplicial complexes with minimum degree sequences, which is a generalisation of the usual minimum degree condition. They determine the essentially best possible minimum degree sequence for finding an almost perfect matching. Furthermore, their main result establishes the stability property: under the same degree assumption, if there is no perfect matching then there must be a space or divisibility barrier. This allows the use of the stability method in proving exact results. Besides recovering previous results, the authors apply our theory to the solution of two open problems on hypergraph packings: the minimum degree threshold for packing tetrahedra in -graphs, and Fischer's conjecture on a multipartite form of the Hajnal-Szemerédi Theorem. Here they prove the exact result for tetrahedra and the asymptotic result for Fischer's conjecture; since the exact result for the latter is technical they defer it to a subsequent paper.

The Optimal Version Of Hua S Fundamental Theorem Of Geometry Of Rectangular Matrices

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Author : Peter Šemrl
language : en
Publisher: American Mathematical Soc.
Release Date : 2014-09-29

The Optimal Version Of Hua S Fundamental Theorem Of Geometry Of Rectangular Matrices written by Peter Šemrl and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-29 with Mathematics categories.

Hua's fundamental theorem of geometry of matrices describes the general form of bijective maps on the space of all m\times n matrices over a division ring \mathbb{D} which preserve adjacency in both directions. Motivated by several applications the author studies a long standing open problem of possible improvements. There are three natural questions. Can we replace the assumption of preserving adjacency in both directions by the weaker assumption of preserving adjacency in one direction only and still get the same conclusion? Can we relax the bijectivity assumption? Can we obtain an analogous result for maps acting between the spaces of rectangular matrices of different sizes? A division ring is said to be EAS if it is not isomorphic to any proper subring. For matrices over EAS division rings the author solves all three problems simultaneously, thus obtaining the optimal version of Hua's theorem. In the case of general division rings he gets such an optimal result only for square matrices and gives examples showing that it cannot be extended to the non-square case.

Imprimitive Irreducible Modules For Finite Quasisimple Groups

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Author : Gerhard Hiss
language : en
Publisher: American Mathematical Soc.
Release Date : 2015-02-06

Imprimitive Irreducible Modules For Finite Quasisimple Groups written by Gerhard Hiss and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-02-06 with Mathematics categories.

Motivated by the maximal subgroup problem of the finite classical groups the authors begin the classification of imprimitive irreducible modules of finite quasisimple groups over algebraically closed fields K. A module of a group G over K is imprimitive, if it is induced from a module of a proper subgroup of G. The authors obtain their strongest results when char(K)=0, although much of their analysis carries over into positive characteristic. If G is a finite quasisimple group of Lie type, they prove that an imprimitive irreducible KG-module is Harish-Chandra induced. This being true for \rm char(K) different from the defining characteristic of G, the authors specialize to the case char(K)=0 and apply Harish-Chandra philosophy to classify irreducible Harish-Chandra induced modules in terms of Harish-Chandra series, as well as in terms of Lusztig series. The authors determine the asymptotic proportion of the irreducible imprimitive KG-modules, when G runs through a series groups of fixed (twisted) Lie type. One of the surprising outcomes of their investigations is the fact that these proportions tend to 1, if the Lie rank of the groups tends to infinity. For exceptional groups G of Lie type of small rank, and for sporadic groups G, the authors determine all irreducible imprimitive KG-modules for arbitrary characteristic of K.

Special Values Of Automorphic Cohomology Classes

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Author : Mark Green
language : en
Publisher: American Mathematical Soc.
Release Date : 2014-08-12

Special Values Of Automorphic Cohomology Classes written by Mark Green and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-08-12 with Mathematics categories.

The authors study the complex geometry and coherent cohomology of nonclassical Mumford-Tate domains and their quotients by discrete groups. Their focus throughout is on the domains which occur as open -orbits in the flag varieties for and , regarded as classifying spaces for Hodge structures of weight three. In the context provided by these basic examples, the authors formulate and illustrate the general method by which correspondence spaces give rise to Penrose transforms between the cohomologies of distinct such orbits with coefficients in homogeneous line bundles.

Index Theory For Locally Compact Noncommutative Geometries

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Author : A. L. Carey
language : en
Publisher: American Mathematical Soc.
Release Date : 2014-08-12

Index Theory For Locally Compact Noncommutative Geometries written by A. L. Carey and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-08-12 with Mathematics categories.

Spectral triples for nonunital algebras model locally compact spaces in noncommutative geometry. In the present text, the authors prove the local index formula for spectral triples over nonunital algebras, without the assumption of local units in our algebra. This formula has been successfully used to calculate index pairings in numerous noncommutative examples. The absence of any other effective method of investigating index problems in geometries that are genuinely noncommutative, particularly in the nonunital situation, was a primary motivation for this study and the authors illustrate this point with two examples in the text. In order to understand what is new in their approach in the commutative setting the authors prove an analogue of the Gromov-Lawson relative index formula (for Dirac type operators) for even dimensional manifolds with bounded geometry, without invoking compact supports. For odd dimensional manifolds their index formula appears to be completely new.

Analysis Of The Hodge Laplacian On The Heisenberg Group

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Author : Detlef Muller
language : en
Publisher: American Mathematical Soc.
Release Date : 2014-12-20

Analysis Of The Hodge Laplacian On The Heisenberg Group written by Detlef Muller and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-12-20 with Mathematics categories.

The authors consider the Hodge Laplacian \Delta on the Heisenberg group H_n, endowed with a left-invariant and U(n)-invariant Riemannian metric. For 0\le k\le 2n+1, let \Delta_k denote the Hodge Laplacian restricted to k-forms. In this paper they address three main, related questions: (1) whether the L^2 and L^p-Hodge decompositions, 1

A Homology Theory For Smale Spaces

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Author : Ian F. Putnam
language : en
Publisher: American Mathematical Soc.
Release Date : 2014-09-29

A Homology Theory For Smale Spaces written by Ian F. Putnam and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-29 with Mathematics categories.

The author develops a homology theory for Smale spaces, which include the basics sets for an Axiom A diffeomorphism. It is based on two ingredients. The first is an improved version of Bowen's result that every such system is the image of a shift of finite type under a finite-to-one factor map. The second is Krieger's dimension group invariant for shifts of finite type. He proves a Lefschetz formula which relates the number of periodic points of the system for a given period to trace data from the action of the dynamics on the homology groups. The existence of such a theory was proposed by Bowen in the 1970s.