Stephen R. Doty, Karin Erdmann, and Daniel K. Nakano

Extensions of modules over Schur algebras, symmetric groups
and Hecke algebras

Abstract. We study the relation between the cohomology of
the general linear and symmetric groups and their respective
quantizations, using Schur algebras and standard homological
techniques to build appropriate spectral sequences. As our
methods fit inside a much more general context within the
theory of finite dimensional algebras, we develop our results
first in that general setting, and then specialize to the
above situations. From this we obtain new proofs of several
known results in modular representation theory of symmetric
groups. Moreover, we reduce certain questions about computing
extensions for symmetric groups and Hecke algebras to 
questions about extensions for general linear groups and
their quantizations.