Tuesday, July 9, 14:00, 7.527

Amrutha Parola (Chennai Mathematical Institute), Cyclic characters and locally invariant vectors in representations of symmetric groups and alternating groups.

Abstract:

The cyclic characters of a group G are the characters induced from its cyclic subgroups. For classical Coxeter groups, Kraskiewicz and Weyman worked out the decomposition into irreducible characters of characters induced from the cyclic subgroup generated by a Coxeter element. The cyclic characters of S_n are described in terms of a statistic on the Young tableaux called the multi major index. In this talk, we will see a description of the cyclic characters of the alternating group. Then we use these description to characterize locally G-invariant vectors when G is symmetric group and alternating group. This is joint work with Amritanshu Prasad and Velmurugan S.