Lecture (2008)
| Speaker | Stephen Doty （Loyola University） |
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| Title | Generalized (q)-Schur algebras |
| Date | May 12 (Mon)2008 ～ May 16 (Fri)2008 |
| Abstract | 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. |
| Speaker | Peter Fiebig (Freiberg University) |
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| Title | Sheaves on affine flag manifolds and Lusztig's conjecture |
| Date | May 12 (Mon)2008 ～ May 16 (Fri)2008 |
| Abstract | The theory of moment graphs is one of the main ingredients in a recent new proof of Lusztig's multiplicity conjecture for quantum groups and for algebraic groups in almost all characteristics. In this series of lectures I will survey the theory of moment graphs and explain how it can be used to link the topology of affine flag manifolds to Lusztig's conjecture. |