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Number Theory Seminar

Title: A Multiplicity one theorem and Gelfand criterion
Speaker: Shiv Prakash Patel (IIT Delhi)
Date: 26 November 2021
Time: 2 pm
Venue: Microsoft Teams (Online)

Let $H$ be a subgroup of a group $G$. For an irreducible representation $\sigma$ of $H$, the triple $(G,H, \sigma)$ is called a Gelfand triple if $\sigma$ appears at most once in any irreducible representation of $G$. Given a triple, it is usually difficult to determine whether a given triple is a Gelfand triple. One has a sufficient condition which is geometric in nature to determine if a given triple is a Gelfand triple, called Gelfand criterion. We will discuss some examples of the Gelfand triple which give us multiplicity one theorem for non-degenerate Whittaker models of ${\mathrm GL}_n$ over finite chain rings, such as $\mathbb{Z}/p^n\mathbb{Z}$. This is a joint work with Pooja Singla.

Contact: +91 (80) 2293 2711, +91 (80) 2293 2265 ;     E-mail: chair.math[at]iisc[dot]ac[dot]in
Last updated: 08 Dec 2021