Dear all,
The next talk is by Nishu Kumari, a graduate student in IISc, Bangalore. The announcement is below.
Talk Announcement
Title: Factorization of Classical Characters twisted by Roots of Unity
Schur polynomials are the characters of irreducible representations of classical groups of type A parametrized by partitions. For a fixed integer $t \geq 2$ and a primitive $t$'th root of unity \omega, Schur polynomials evaluated at elements $\omega^{k} x_i$ for $0 \leq k \leq t-1$ and $1 \leq i \leq n$, were considered by D. J. Littlewood (AMS press, 1950) and independently by D. Prasad (Israel J. Math., 2016). They characterized partitions for which the specialized Schur polynomials are nonzero and showed that if the Schur polynomial is nonzero, it factorizes into characters of smaller classical groups of type A.
Speaker: Nishu Kumari (IISc, Bangalore)
When: Thursday, November 17, 2022 - 4:00 PM - 5:00 PM (IST)
Where: Zoom. Please write to the organisers for the link.
Live Link: https://youtu.be/nFarazOy7eI
Tea or Coffee: Please bring your own.
Abstract:
In this talk, I will present a generalization of the factorization result to the characters of classical groups of type B, C and D. We give a uniform approach for all cases. The proof uses Cauchy-type determinant formulas for these characters and involves a careful study of the beta sets of partitions. This is joint work with A. Ayyer and is available here. (Preprint: https://arxiv.org/abs/2109.
