Combinatorial formulae for induced representations of affine Hecke algebras

par Eloise Little (University of Sydney)

vendredi 2 déc. 2022, 10:30 → 11:30 Europe/Paris

E2 1180 (Tours)

In this talk I will construct and give examples of a combinatorial approach to finding the explicit matrix entries of representations of affine Hecke algebras induced from 1-dimensional representations of Levi subalgebras. This combinatorial approach is in terms of "alcove paths" in the associated affine Weyl group. 

I will first introduce affine Weyl groups and affine Hecke algebras, and then explain the construction of the induced representations. Next I will explain the combinatorial formulas, using alcove walks, of the principal series representation matrix entries and the matrix entries of the induced representations. 

This is joint work with Jeremie Guilhot and James Parkinson.