Demazure crystals and tensor products of perfect Kirillov-Reshetikhin crystals with various levels

Details Demazure crystals and tensor products of perfect Kirillov-Reshetikhin crystals with various levels Demazure crystals and tensor products of perfect Kirillov-Reshetikhin crystals with various levels

2011-08-16

arxiv.org/abs/1108.3139v1

Mathematics

Quantum Algebra

26 pages

Scientific paper

In this paper, we study a tensor product of perfect Kirillov-Reshetikhin crystals (KR crystals, for short) whose levels are not necessarily equal. We show that, by tensoring with a certain highest weight element, such a crystal becomes isomorphic as full subgraphs to a certain disjoint union of Demazure crystals contained in a tensor product of highest weight crystals. Moreover, we show that this isomorphism preserves their gradings, where the grading on the tensor product of KR crystals is given by the energy function, and that on the other side is given by the minus of the action of the degree operator.

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