Archimedean L-functions and Hecke-Baxter operators
Organizers
Speaker
Time
Thursday, April 24, 2025 12:15 PM - 1:00 PM
Venue
A4-1
Abstract
For an admissible representation of a split real group GL(n,R), one might canonically attach a local Archimedean L-factor, a function in a single complex variable capturing data of the original representation. Introducing this specific L-function is motivated by deep connections with the theory of zeta-functions of global number fields. In particular, the local L-factors of representations of non-compact groups play an essential role in formulation of the Langlands correspondence for these groups. However, the classical construction of the Archimedean L-factors follows some round-about strategy. In my talk I discuss the so-called Hecke-Baxter operator, an element of the spherical Hecke algebra associated with the Gelfand pair (GL(n,R), O(n)). This element is specified by the property that its action on a O(n)-fixed vector in a principal series GL(n,R)-representation reproduces the Archimedean L-function attached to this representation. This is a joint project with A.Gerasimov and D. Lebedev.
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.