Date & Time: Thursday, February 12, 2015, 14:30-16:00.
Venue: Room 216
Title: On the representation theory of G wreath S_n
Speaker: Murali Srinivasan, IIT Bombay
Abstract: In the Vershik-Okounkov approach to the complex irreducible representations of $S_n$ and $G wreath S_n$ we parametrize the irreducible representations and their bases by spectral objects rather than combinatorial objects and then, at the end, give a bijection between the spectral and combinatorial objects. The fundamental ideas are similar in both cases but there are additional technicalities involved in the $G wreath S_n$ case. This was carried out by Pushkarev.
The present work gives a fully detailed exposition of Pushkarev's theory. For the most part we follow the original but our definition of a Gelfand-Tsetlin subspace, based on a multiplicity free chain of subgroups, is slightly different and leads to a more natural development of the theory.
We also work out in detail a nontrivial example, the wreath product action on generalized Boolean algebras, from this viewpoint. (Joint work with A. Mishra).