Algebraic methods: Lie groups, quantum groups
نویسنده
چکیده
These notes concentrate on the paradigm of spherical functions on Riemannian symmetric spaces. This paradigm has led to the notion of special functions associated with root systems. The first sections deal with older work on the interaction between spherical functions on rank one symmetric spaces and special functions (q=1) in one variable. The (spectacular) developments in the higher rank case and the q c.q. quantum case are summarized in two charts: one for q = 1 and one for the q-case. See also the related lectures by W. Miller and C. Dunkl during this program (at http://www.ima.umn.edu/digital-age/).
منابع مشابه
Algebraic Groups, Lie Groups, and their Arithmetic Subgroups
This work is a modern exposition of the theory of algebraic group schemes, Lie groups, and their arithmetic subgroups. It supersedes Algebraic Groups and Arithmetic Groups. This file only contains the front matter. For the rest, see Single paper copies for noncommercial personal use may be made without explicit permission from the copyright holder. Preface For one who attempts to unravel the st...
متن کاملInduced Representations of Hopf Algebras: Applications to Quantum Groups at Roots of 1
Introduction This paper serves three purposes. The first is to build up a connection between the representation theories of the quantum enveloping algebra U of a semisimple Lie algebra and the quantum groups defined in [15]. The second one is to study the structure of the derived functors of the induction functor, defined in [1]. At each integral weight, these derived functors give rise to cert...
متن کاملNEW METHODS FOR CONSTRUCTING GENERALIZED GROUPS, TOPOLOGICAL GENERALIZED GROUPS, AND TOP SPACES
The purpose of this paper is to introduce new methods for constructing generalized groups, generalized topological groups and top spaces. We study some properties of these structures and present some relative concrete examples. Moreover, we obtain generalized groups by using of Hilbert spaces and tangent spaces of Lie groups, separately.
متن کاملIrreducible Modular Representations of Finite and Algebraic Groups
In these notes we outline some aspects of the modular representation theories of finite groups of Lie type in defining and cross-characteristics, with particular interest paid to how these theories relate to the modular representation theory of algebraic groups and the (characteristic 0) representation theory of Lie algebras and quantum groups. We begin by summarizing some classical results on ...
متن کاملOn quantization of Semenov-Tian-Shansky Poisson bracket on simple algebraic groups
Let G be a simple complex algebraic group equipped with a factorizable Poisson Lie structure. Let U~(g) be the corresponding quantum group. We study U~(g)-equivariant quantization C~[G] of the affine coordinate ring C[G] along the Semenov-Tian-Shansky Poisson Lie bracket. For a simply connected group G we prove an analog of the KostantRichardson theorem stating that C~[G] is a free module over ...
متن کاملClassification of low dimensional Lie super-bialgebras
A thorough analysis of Lie super-bialgebra structures on Lie superalgebras osp(1; 2) and super e(2) is presented. Combined technique of computer algebraic computations and a subsequent identification of equivalent structures is applied. In all the cases Poisson-Lie brackets on supergroups are found. Possibility of quantizing them in order to obtain quantum groups is discussed. It turns out to b...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2005