A combinatorial formula expressing periodic \$R\$-polynomials. (arXiv:1603.02778v2 [math.RT] UPDATED)

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.查看全文

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 你的名字 留空匿名提交 你的Email或网站 用户可以联系你 标题 简单描述 内容 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.