Algebra Seminar: Gurevich -- Decomposition rules for representations of p-adic groups

 Maxim Gurevich (Weizmann Institute) 

Friday 25 November, 11am-12pm, Place: Carslaw 375 

Decomposition rules for representations of p-adic groups 

What are the irreducible constituents of a smooth representation of a p-adic group that
is constructed through parabolic induction? In the case of GL_n this is the study of the
multiplicative behaviour of irreducible representations in the Bernstein-Zelevinski
ring.  Strikingly, the same decomposition problem can be reformulated through various
Lie-theoretic settings of type A, such as canonical bases in quantum groups,
representations of affine Hecke algebras, quantum affine Lie algebras, or more recently,
KLR algebras.  While partially touching on some of these phenomena, I will present new
results on the problem using mostly classical tools.  In particular, we will see how
introducing a width invariant to an irreducible representation can circumvent the
complexity involved in computations of Kazhdan-Lusztig polynomials.