相关论文: IntroSurvey of representation theory
We study three fundamental topics in the representation theory of disconnected algebraic groups whose identity component is reductive: (i) the classification of irreducible representations; (ii) the existence and properties of Weyl and dual…
The representation theory of the symmetric groups is intimately related to geometry, algebraic combinatorics, and Lie theory. The spin representation theory of the symmetric groups was originally developed by Schur. In these lecture notes,…
We develop quaternionic analysis using as a guiding principle representation theory of various real forms of the conformal group. We first review the Cauchy-Fueter and Poisson formulas and explain their representation theoretic meaning. The…
These notes are based on a course given at the EPFL in May 2005. It is concerned with the representation theory of Hecke algebras in the non-semisimple case. We explain the role that these algebras play in the modular representation theory…
Following the general idea of Schur--Weyl scheme and using two suitable symmetric groups (instead of one), we try to make more explicit the classical problem of decomposing tensor representations of finite and infinite symmetric groups into…
This book is an introduction to a fast developing branch of mathematics - the theory of representations of groups. It presents classical results of this theory concerning finite groups.
The interrelations between the inverse problems of the representation theory and the categorical representation theory are discussed.
We find and propose an explanation for a large variety of modularity-related symmetries in problems of 3-manifold topology and physics of 3d $\mathcal{N}=2$ theories where such structures a priori are not manifest. These modular structures…
We give a general definition of classical and quantum groups whose representation theory is "determined by partitions" and study their structure. This encompasses many examples of classical groups for which Schur-Weyl duality is described…
This is an elementary introduction to the representation theory of finite semigroups. We illustrate the Clifford-Munn correspondence between the representations of a semigroup and the representations of its maximal subgroups. The emphasis…
The modular representation theory of finite groups has its origins in the work of Richard Brauer. In this survey article we first discuss the work being done on some outstanding conjectures in the theory. We then describe work done in the…
There are two approaches to projective representation theory of symmetric and alternating groups, which are powerful enough to work for modular representations. One is based on Sergeev duality, which connects projective representation…
We derive the representation theory of $SU(2)$ from the expository theory of Lie groups and Lie algebras. Based on this, the mathematics of non-relativistic quantum mechanics of a spin $\frac{1}{2}$ particle are described from a…
Beginning from a discussion of the known most fundamental dynamical structures of the Standard Model of physics, extended into the realms of mathematics and theory by the concept of "supersymmetry" or "SUSY," an introduction to efforts to…
These notes of a course given at IRMA in April 2009 cover some aspects of the representation theory of fundamental groups of manifolds of dimension at most 3 in compact Lie groups, mainly $\su$. We give detailed examples, develop the…
We survey some important results concerning the finite--dimensional representations of the loop algebra of a simple complex Lie algebra, and their twisted loop subalgebras. In particular, we review the parametrization and description of the…
We review the recent development in the representation theory of the $W_{1+\infty}$ algebra. The topics that we concern are, Quasifinite representation, Free field realizations, (Super) Matrix Generalization, Structure of subalgebras such…
Linearity allows several versions of reality to simultaneously exist in the state vector. But it implies that there is no interaction between versions, and that there will never be perception of more than one version. It also implies, in…
A diverse collection of fusion categories may be realized by the representation theory of quantum groups. There is substantial literature where one will find detailed constructions of quantum groups, and proofs of the…
These notes provide a concise introduction to the representation theory of reductive algebraic groups in positive characteristic, with an emphasis on Lusztig's character formula and geometric representation theory. They are based on the…