Cristian Lenart ; Satoshi Naito ; Daisuke Sagaki ; Anne Schilling ; Mark Shimozono - A uniform model for Kirillov―Reshetikhin crystals

dmtcs:12790 - Discrete Mathematics & Theoretical Computer Science, January 1, 2013, DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013) - https://doi.org/10.46298/dmtcs.12790
A uniform model for Kirillov―Reshetikhin crystalsArticle

Authors: Cristian Lenart 1; Satoshi Naito 2; Daisuke Sagaki 3; Anne Schilling 4; Mark Shimozono 5

  • 1 Department of Mathematics and Statistics [Albany-USA]
  • 2 Department of Mathematics [Tokyo]
  • 3 Institute of Mathematics, University of Tsukuba
  • 4 Department of Mathematics [Univ California Davis]
  • 5 Department of Mathematics [Blacksburg]

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.


Volume: DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013)
Section: Proceedings
Published on: January 1, 2013
Imported on: November 21, 2016
Keywords: Parabolic quantum Bruhat graph,Kirillov―Reshetikhin crystals,energy function,Lakshmibai―Seshadri paths,Macdonald polynomials.,[INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]

Consultation statistics

This page has been seen 61 times.
This article's PDF has been downloaded 60 times.