Chennai Combinatorics Colloquium Series
Speaker: Arvind Ayyer, IISc Bengaluru
Date: Friday, 4 July 2025
Time: 3:30 PM
Venue: Seminar Hall
Factorization of classical characters twisted by roots of unity
Arvind Ayyer
IISc Bengaluru.
04-07-25

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Abstract

Schur polynomials are an important family of symmetric polynomials arising as characters of the general linear group. I will begin by explaining their importance in the theory of symmetric polynomials and various formulas for them. I will then explain a classical result of Littlewood -- rediscovered many times -- about the factorization of the Schur polynomial \[ s_\lambda(x_1, \dots, x_n, \omega x_1, \dots, \omega x_n, \dots, \omega^{t-1} x_1, \dots, \omega^{t-1} x_1), \] where $\omega$ is a primitive $t$'th root of unity. Time permitting, I will explain joint work with N. Kumari (J. Alg., 2022), where we extend this work to other classical characters. No background will be assumed.