# Alexey Petukhov

## "Multiplicity-Free Modules of Reductive Groups"

 Date: Mon, October 10, 2016 Time: 15:00 Place: Seminar Room (120), Research I

Abstract: Let $$G$$ be a reductive algebraic group, $$V$$ be a simple finite-dimensional $$G$$-module, and $$H$$ be a reductive subgroup of $$G$$. The restriction $$V|_H$$ of $$V$$ to $$H$$ is no longer simple in general but is a direct sum of simple $$H$$-modules. The triple $$(G, V; H)$$ is called multiplicity free if the multiplicities of the simple $$H$$-constituents in $$V|_H$$ are either $$0$$ or $$1$$.
In my talk I will describe some classes of multiplicity free triples and provide a connection between such triples and $$H$$-spherical actions on $$G$$-flag varieties. The output will be a class of multiplicity free modules together with the respective decompositions of $$V|_H$$ into simple constituents.
Also I would like to ask whether or not you could provide bibliographical data for the article "On ideals in $$U\big(\text{sl}(\infty)\big)$$, $$U\big(\text{o}(\infty)\big)$$, $$U\big(\text{sp}(\infty)\big)$$." It is related to the annual report request for the Premet's grant.