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arXiv · 1211.6019

A uniform model for Kirillov-Reshetikhin crystals. Extended abstract

Cristian Lenart·Satoshi Naito·Daisuke Sagaki·Anne Schilling·Mark Shimozono
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Abstract

We present a uniform construction of tensor products of one-column Kirillov-Reshetikhin (KR) crystals in all untwisted affine types, which uses a generalization of the Lakshmibai-Seshadri paths (in the theory of the Littelmann path model). This generalization is based on the graph on parabolic cosets of a Weyl group known as the parabolic quantum Bruhat graph. A related model is the so-called quantum alcove model. The proof is based on two lifts of the parabolic quantum Bruhat graph: to the Bruhat order on the affine Weyl group and to Littelmann's poset on level-zero weights. Our construction leads to a simple calculation of the energy function. It also implies the equality between a Macdonald polynomial specialized at t=0 and the graded character of a tensor product of KR modules.

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BibTeXRIS

Cristian Lenart, Satoshi Naito, Daisuke Sagaki, Anne Schilling, Mark Shimozono. 2012-11-26. A uniform model for Kirillov-Reshetikhin crystals. Extended abstract. https://arxiv.org/abs/1211.6019

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