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Approximating combinatorial representation theory
Algebra & Discrete Mathematics| Speaker: | Nat Thiem, Stanford University |
| Location: | 1147 MSB |
| Start time: | Fri, Apr 20 2007, 3:10PM |
Description
Combinatorial representation theory has made remarkable progress in our
understanding of groups, algebras, and their many applications. However, there are
still many examples of algebraic structures -- such as the group of unipotent
upper-triangular matrices over a finite field U_n -- where a complete understanding of
the representation theory is provably unknowable. This talk explores an alternative
to a complete understanding by developing a notion of an approximate representation
theory (or super representation theory). We will show that for a family of groups
that generalize U_n, the natural approximation not only is understandable, but we even
obtain character formulas. Along the way, I will also mention some of the many open
questions in this new area of research. This is joint work with P. Diaconis.