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Crystal Bases for type D Kirillov-Reshetikhin modules
Algebra & Discrete Mathematics| Speaker: | Philip Sternberg, UC Davis |
| Location: | 693 Kerr |
| Start time: | Fri, Jan 16 2004, 12:10PM |
Description
Kirillov-Reshetikhin modules are a family of modules over
quantum affine algebras. In this talk, we consider K-R modules over
algebras of type $D_n^{(1)}$ associated with an integer multiple of the
second fundamental weight. Combinatorially, this means that the vertices
of the crystal graph of the module are indexed by rectangular tableaux
with two rows. We will first specify what constitutes a legal tableau
in this context, and then describe the action of the quantum affine algebra
on the associated module elements. Finally, we will see some facts which
strongly suggest that these crystals are perfect.