BIMSA >
BIMSA Integrable Systems Seminar
On matrix element representation of the GKZ hypergeometric functions
On matrix element representation of the GKZ hypergeometric functions
Organizers
Speaker
Time
Tuesday, March 12, 2024 4:00 PM - 5:00 PM
Venue
A6-101
Online
Zoom 873 9209 0711
(BIMSA)
Abstract
In the talk, I shall present our joint paper with A.Gerasimov and D.Lebedev. In this paper, 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 non-reductive Lie algebras $L(N)$ of oscillator type. The Whittaker functions associated with principal series representations of $gl(n,R)$ being special cases of GKZ hypergeometric functions, thus admit along with a standard matrix element representations associated with reductive Lie algebra $gl(n,R)$, another matrix element representation in terms of $L(n(n-1))$.
Speaker Intro
Sergey Oblezin received his PhD at Moscow Institute of Physics and Technology in 2004. Education in Moscow and work experience at the Alikhanov Institute for Theoretical and Experimental Physics shaped his intra-disciplinary vision in mathematics, based on a unique and mutually transformative synthesis of quantum physics and mathematics. At early stage, his research achievements were recognized by several awards including two Russian Federation President Fellowships for young mathematicians (in 2007-2008 and 2008-2009). In 2009-2012, Sergey's research was awarded by the Pierre Deligne Prize (supported by P.Deligne's Balzan Prize, 2004). In 2013-17 Sergey's project "Topological field theories, Baxter operators and the Langlands programme" was supported by the Established Career EPSRC grant (UK). During 2015-2023, Sergey was an Associate Professor in Geometry at the University of Nottingham (UK), before taking his current full-time Professor position at BIMSA in 2024. Sergey Oblezin is working on a long term research project devoted to transferring and developing methods and constructions of quantum physics to the Langlands Program. His research interests include representation theory, harmonic analysis and their interactions with number theory and mathematical physics.