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q-analogues of tensor product multiplicities

Algebra & Discrete Mathematics

Speaker: Lipika Deka, Math UC Davis
Location: 693 Kerr
Start time: Thu, Feb 13 2003, 12:10PM

I am going to talk about how to get tensor product multiplicities using crystals and then how to obtain q-analogues of these using the energy function which is a statistic on the elements of tensor product of affine crystals. Mostly I will talk about the type A_n case, but I will mention what's the story in type D_n Just to make it interesting let me mention that in this analogy Kostka polynomial becomes the q-analogue of the Kostka numbers using the energy statistic in a special case of type A_n.