ODTÜ-BİLKENT
ALGEBRAIC GEOMETRY SEMINAR

“Multiplicative
Generators for the Hecke ring of the Gelfand Pair (S(2n),
H(n))”

by

KÜRŞAT AKER

Feza Gursey Institute

Abstract: For a given positive integer n, Gelfand
pair (S(2n), H(n)) resembles the symmetric group S(n)
in numerous ways. Here, H(n) is a hyperoctahedral
subgroup of the symmetric group S(2n). In this talk, we will exhibit a new
similarity between the Hecke ring of the pair (S(2n), H(n)) and the center of the
integral group ring of S(n).

Multiplicative generators for centers
of integral symmetric groups were first identified by Farahat
and Higman, which were later shown to be elementary
symmetric polynomials in the celebrated Young-Jucys-Murphy
elements by Jucys. In this talk, we will present a
set of multiplicative generators for the Hecke ring
of (S(2n), H(n)), affirming a conjecture of Matsumoto, who showed these
elements are elementary symmetric polynomials evaluated at odd Young-Jucys-Murphy elements after projecting from the integral
group ring of S(2n) to the Hecke ring of (S(2n),H(n)).
This is a joint work with Mahir Bilen
Can, Tulane University.

* Reference: http://front.math.ucdavis.edu/1009.5373

Date:  17 December 2010 Friday

Time: 15:40

Place: Bilkent University, Mathematics Seminar Room SA-141

Tea and cookies will be served before the
talk.