Extension Groups between Specht Modules of Type ``A'' Hecke Orders
by
Marcos Soriano
University of Stuttgart

Let R be the ring of Laurent polynomials with integral coefficients, let K be its quotient field, the function field in one variable q over the rationals.

We study the generic Iwahori-Hecke algebra H associated to the symmetric group on n letters, considered as an R-order embedded in the separable algebra A : = K\otimes_RH. We will concentrate on giving the rather simple proof that the extension groups Ext¹_H(S₁, S₂) between two different Specht modules are finitely generated Z-torsionfree, a remarkable fact. The very general proof also applies to other situations.

We will introduce the key ingredients necessary for the proof, stressing the role played by the Higman ideal of H. Actually one recovers from the proof a (``classical'') way of computing extension groups, which was our starting point, motivated by some beautiful formulas found by M. Künzer for the integral group ring of the symmetric group. We shall give some examples based on the ``lifting'' to the Hecke order of these formulas.

Date received: July 28, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cafe-46.