Event № 291
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 the problem can be formulated as a study of the multiplicative behavior of irreducible representations in the so-called Bernstein-Zelevinski ring.
I will try to convey the idea that such problems are in fact universal in Lie theory. The theory of Kazhdan-Lusztig polynomials points on intriguing equivalences between several settings, such as representations of Lie algebras, affine Hecke algebras, canonical bases in quantum groups and more recently KLR algebras. All of which give different tools and points of view on similar phenomena.