Kirillov–Reshetikhin crystals, energy function and the combinatorial R-matrix

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• 作者：Deniz Kus
• 关键词：KR crystal ; Energy function ; R ; matrix
• 刊名：Journal of Algebraic Combinatorics
• 出版年：2016
• 出版时间：February 2016
• 年：2016
• 卷：43
• 期：1
• 页码：45-74
• 全文大小：687 KB
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  4.Hatayama, G., Kuniba, A., Okado, M., Takagi, T., Yamada, Y. (1999) Remarks on fermionic formula. In: Recent Developments in Quantum Affine Algebras and Related Topics (Raleigh, NC, 1998), volume 248 of Contemporary Mathematics, pp. 243–291. American Mathematical Society, Providence, RI (1999)
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• 作者单位：Deniz Kus (1)
  
  1. Mathematisches Institut, Universität zu Köln, Cologne, Germany
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Combinatorics
  Convex and Discrete Geometry
  Order, Lattices and Ordered Algebraic Structures
  Computer Science, general
  Group Theory and Generalizations
  
• 出版者：Springer U.S.
• ISSN：1572-9192

文摘

We study the polytope model for the affine type A Kirillov–Reshetikhin crystals and prove that the action of the affine Kashiwara operators can be described in a remarkably simple way. Moreover, we investigate the combinatorial R-matrix on a tensor product of polytopes and characterize the map explicitly on the highest weight elements. We further give a formula for the local energy function and provide an alternative proof for the perfectness. We determine for any dominant highest weight element \(\Lambda \) of level \(\ell \) the elements \(b_{\Lambda }, b^{\Lambda }\) involved in the definition of perfect crystals and give an explicit description of the ground-state path in the tensor product of polytopes.