Aarhus University Seal / Aarhus Universitets segl

Seminar by Anatol Kirillov (Kyoto University)

Title: Algebraic and combinatorial properties of Dunkl operators at critical level

2013.10.21 | Christine Dilling

Date Wed 17 Aug
Time 16:00 17:00
Location Aud. D3


The Dunkl operators have been introduced by C.Dunkl in the middle if 80's of last century, since that time have found numerous applications in Mathematics and Mathematical Physics. There are three kinds of Dunkl operators, namely, rational, trigonometric and elliptic. 

In my talk I introduce a certain noncommutative inhomogeneous quadratic algebra and distinguish set of mutually commuting element in it in such a way that three kinds of Dunkl operators a t critical level will corresponds to some representations of the quadratic algebra in question. The main purpose of my talk is to explain some algebraic and combinatorial properties of that "universal Dunkl elements" (UDE), as well as to outlook surprising connections of UDE with quantum and classical Schubert calculus, elliptic hypergeometric series, volume of Chan-Robbins polytopes and so on.