The speaker is
Prof. Amritanshu Prasad from IMSc, Chennai. The following are the
details.
Title: Polynomials as Characters of Symmetric Groups.
Time: 7pm, Tuesday, September 1, 2020 (gate opens at 6:45pm).
Google meet link: meet.google.com/prm-feow-zwm.
Phone: (US) +1 740-239-3129 PIN: 706 683 026#
Abstract: Treating the variable $X_i$ as the number of $i$-cycles in a
permutation allows a polynomial in $X_1, X_2,\dotsc$ to be regarded as a
class function of the symmetric group $S_n$ for any positive integer $n$.
We present a simple formula for computing the average and signed average
of such a class function over the symmetric group. We use this formula to
investigate the dimension of $S_n$-invariant and $S_n$-sign-equivariant
vectors in polynomial representations of general linear groups.
This talk is based on joint work with Sridhar P Narayanan, Digjoy Paul,
and Shraddha Srivastava. Some of these results are available in the
preprint available at:
http://arxiv.org/abs/2001.04112.