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Bijection between rigged configurations and crystals for affine Lie algebras of type {A_n}^{(1)} and {D_n}^{(1)}.

Algebra & Discrete Mathematics

Speaker: Lipika Deka, UC Davis
Location: 593 Kerr
Start time: Thu, May 2 2002, 3:10PM

I will talk about a bijection between crystals and rigged configurations. Crystals come from the corner transfer matrix method and rigged configurations originate from the Bethe Ansatz of exactly solvable lattice models in Statistical Mechanics. The correspondence between these two methods is not rigorous, but knowing the bijection between crystals and rigged configurations makes this correspondense precise on the combinatorial and representation theoretic level. The bijection exists for any affine Kac-Moody algebra. By some embedding theorems, it is enough to know the bijection for type {A_n}^{(1)} and {D_n}^{(1)}. The bijections for type {A_n}^{(1)} are well understood. My talk will focus on conjectured bijections for type {D_n}^{(1)}.

This is the first of 2 parts (continues on May 9th) May 2nd we have a second talk by Prof. Sinai Robins from Temple University at 4:00pm.