## Anne Schilling ; Peter Tingley - Demazure crystals and the energy function

dmtcs:2959 - Discrete Mathematics & Theoretical Computer Science, January 1, 2011, DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011) - https://doi.org/10.46298/dmtcs.2959
Demazure crystals and the energy function

Authors: Anne Schilling ; Peter Tingley

There is a close connection between Demazure crystals and tensor products of Kirillov–Reshetikhin crystals. For example, certain Demazure crystals are isomorphic as classical crystals to tensor products of Kirillov–Reshetikhin crystals via a canonically chosen isomorphism. Here we show that this isomorphism intertwines the natural affine grading on Demazure crystals with a combinatorially defined energy function. As a consequence, we obtain a formula of the Demazure character in terms of the energy function, which has applications to nonsymmetric Macdonald polynomials and $q$-deformed Whittaker functions.

Volume: DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011)
Section: Proceedings
Published on: January 1, 2011
Imported on: January 31, 2017
Keywords: Demazure crystals,affine crystals,nonsymmetric Macdonald polynomials,Whittaker functions,[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO],[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]
Fundings :
Source : OpenAIRE Research Graph
• PostDoctoral Research Fellowship; Funder: National Science Foundation; Code: 0902649
• FRG: Collaborative Research: Affine Schubert Calculus: Combinatorial, geometric, physical, and computational aspects; Funder: National Science Foundation; Code: 0652652
• Affine Combinatorics; Funder: National Science Foundation; Code: 1001256
• FRG: Collaborative Research: Affine Schubert Calculus: Combinatorial, geometric, physical, and computational aspects; Funder: National Science Foundation; Code: 0652641