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How to multiply matrices the hard way: braid relations for $GL_n(F_q)$ and the RSK-correspondence
Student-Run Research Seminar| Speaker: | Nat Thiem, Stanford University |
| Location: | 693 Kerr |
| Start time: | Wed, Dec 8 2004, 12:10PM |
The symmetric group has provided a combinatorial motivation for many areas of representation theory, leading to an explosion of (modified) braids, partitions, and tableaux throughout Lie theory.
This talk begins with the classical connection between braid diagrams and the representation theory of the symmetric group via the RSK-correspondence, and explores generalizations of this model to the general linear group over a finite field ($GL_n(F_q)$). To accomplish these tasks, we use the reduced row echelon form to view matrices as braid-like diagrams and then approximate an RSK-correspondence for $GL_n(F_q)$ with a family of Hecke algebras.