Related papers: Special functions, KZ type equations and Represent…
These are lecture notes that arose from a representation theory course given by the first author to the remaining six authors in March 2004 within the framework of the Clay Mathematics Institute Research Academy for high school students,…
This is the talk of the second author at the meeting "Topological Methods in Physical Sciences", London, November 2000. We review our work on KZB equations.
These are notes of a graduate course on representations of non-compact semisimple Lie groups given by the author at MIT.
These notes contain part of the lectures of an introductory course on orthogonal polynomials and special functions that I gave in the joint PhD Program in Mathematics UC|UP in the academic years 2015-2016 (at University of Porto) and…
This text is an extended version of the lecture notes for a course on representation theory of finite groups that was given by the authors during several years for graduate and postgraduate students of Novosibirsk State University and…
The point of view of these notes on the topic is to bring out the flavour that Representation Theory is an extension of the first course on Group Theory. We also emphasize the importance of the base field. These notes cover completely the…
Special functions have always played a central role in physics and in mathematics, arising as solutions of particular differential equations, or integrals, during the study of particular important physical models and theories in Quantum…
These lecture notes, adapted from the habilitation thesis of the author, survey in a first part various exact results obtained in the past few decades about KPZ fluctuations in one dimension, with a special focus on finite volume effects…
This is my talk delivered at the workshop 'Automorphic L-Functions and related prpblems' (March 10--13, 2012, Tokyo University). We showed an instance of applications of the theory of automorphic representations to a genuinely traditional…
A representation-theoretic approach to special functions was developed in the 40-s and 50-s in the works of I.M.Gelfand, M.A.Naimark, N.Ya.Vilenkin, and their collaborators. The essence of this approach is the fact that most classical…
Advances in mathematical physics during the 20th century led to the discovery of a relationship between group theory and representation theory with the theory of special functions. Specifically, it was discovered that many of the special…
We give a short introduction to the subject of representation growth and representation zeta functions of groups, omitting all proofs. Our focus is on results which are relevant to the study of arithmetic groups in semisimple algebraic…
We develop representation theory approach to the study of special functions associated with toric varieties. In particular we show that the corresponding special functions are given by matrix elements of certain non-reductive Lie algebras
These are notes from the mini-course given by W. Schmid in June 2003 in the Brussels PQR2003 Euroschool.
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…
These are the notes for a course on representations of quivers for second year students in Paderborn in summer 2007. My aim was to provide a basic introduction without using any advanced methods. It turns out that a good knowledge of linear…
We develop a representation theory approach to the study of generalized hypergeometric functions of Gelfand, Kapranov and Zelevisnky (GKZ). We show that the GKZ hypergeometric functions may be identified with matrix elements of…
The purpose of this informal article is to introduce the reader to some of the objects and methods of the theory of p-adic representations. My hope is that students and mathematicians who are new to the subject will find it useful as a…
These are the notes from the summer school in G\"ottingen sponsored by NATO Advanced Study Institute on Higher-Dimensional Geometry over Finite Fields that took place in 2007. The aim was to give a short introduction on zeta functions over…
In this essay I will give a strictly subjective selection of different types of zeta functions. Instead of providing a complete list, I will rather try to give the central concepts and ideas underlying the theory. This article is going to…