Decomposition of tensor products of Demazure crystals

JOURNAL OF ALGEBRA

卷:546

Article

Kouno, Takafumi¹ 

[1] Tokyo Inst Technol, Dept Math, Meguro Ku, 2-12-1 Oh Okayama, Tokyo 1528551, Japan

关键词: Demazure crystals;    Crystal bases;    Tensor products;    Lakshmibai-Seshadri paths;    Weyl groups;    Key polynomials;   

DOI  :  10.1016/j.jalgebra.2019.11.001

来源: Elsevier

【 摘 要 】

In general, a tensor product of Demazure crystals does not decompose into a disjoint union of Demazure crystals. However, under a certain condition, a tensor product decomposes into a disjoint union of Demazure crystals. In this paper, we introduce a necessary and sufficient condition for every connected component of a tensor product of two Demazure crystals to be isomorphic to some Demazure crystal. Moreover, we consider a recursive formula describing connected components of tensor products of arbitrary Demazure crystals. As an application, we discuss the key positivity problem, which is the problem whether a product of key polynomials is a linear combination of key polynomials with nonnegative integer coefficients or not. Also, we obtain a crystal-theoretic analog of the Leibniz rule for Demazure operators. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free