A combinatorial formula expressing periodic R-polynomials

摘要

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 affuae 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. (C) 2016 Elsevier Inc. All rights reserved.