A combinatorial formula expressing periodic R-polynomials

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• 作者：Satoshi Naito ^{naito@math.titech.ac.jp} ; Hideya Watanabe ^{watanabe.h.at@m.titech.ac.jp}
• 关键词：Periodic Kazhdan&ndash ; Lusztig polynomials ; Periodic R-polynomials ; Generic Bruhat order
• 刊名：Journal of Combinatorial Theory, Series A
• 出版年：2017
• 出版时间：May 2017
• 年：2017
• 卷：148
• 期：Complete
• 页码：197-243
• 全文大小：669 K
• 卷排序：148

文摘

In 1980, Lusztig introduced the periodic Kazhdan–Lusztig polynomials, which are conjectured to have important information about the characters of irreducible modules of a reductive group over a field of positive characteristic, and also about those of an affine Kac–Moody algebra at the critical level. The periodic Kazhdan–Lusztig polynomials can be computed by using another family of polynomials, called the periodic R-polynomials. In this paper, we prove a (closed) combinatorial formula expressing periodic R-polynomials in terms of the “doubled” Bruhat graph associated to a finite Weyl group and a finite root system.