### Seminar in Algebra, Lie Theory, and Geometry

# Alexey Petukhov

### (University of Manchester)

## "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.