概要 |
In type A, Schur algebras were introduced by I. Schur roughly 100 years ago
in order to characterize the polynomial complex representations of GL(n). Around 1980 J.A. Green wrote a monograph
[Springer Lecture Notes 830] explaining their use in understanding the modular representations of general linear
and symmetric groups. Since then an explosion of generalizations have occurred, including the introduction of
q-analogues of Schur algebras by Dipper &James and, independently, Jimbo (with applications to the representations
of the Iwahori-Hecke algebras in type A) and the fundamental theory of "generalized Schur algebras" due to Donkin.
In these talks, I will survey what is known about Schur algebras and q-Schur algebras and how they relate to algebraic groups and quantum groups. |