Braids and tableaux for unipotent Hecke algebras

Nat Thiem, Stanford University

This talk describes (and defines) a family of Hecke algebras that generalize the classical Iwahori-Hecke algebra. While many of the results extend to other groups of Lie type, this talk focuses on the case where the underlying group is the general linear group over a finite field. The main results include: (a) an indexing of the basis elements in terms of row and column degree-sum matrices, (b) a set of braid-like relations for multiplying basis elements, and (c) a generalization of the RSK-correspondence that maps sets of monomial matrices to multi-tableaux.