Return to Colloquia & Seminar listing
Crystal graphs and the representation theory of S_n
Student-Run Research| Speaker: | Monica Vazirani, UC Davis |
| Location: | 693 Kerr |
| Start time: | Wed, Nov 5 2003, 12:10PM |
Description
A crystal graph is a colored directed graph
which appears in the context of Lie algebras and their deformations.
Given two crystal graphs, there is a straightforward rule
for how to tensor them together and get a new crystal graph.
Crystals, and in particular their tensor products,
encode algebraic and combinatorial data
about the representation theory of the associated Lie algebra.
Surprisingly, certain crystals also encode algebraic
properties of a much smaller algebra: the group algebra of
the symmetric group S_n.
I will talk about the representation theoretic information
we can learn about S_n from these crystals, and give some
hints for why this should be so.