Seminar| Institute of Mathematical Sciences
Time: Wednesday, April 22th, 2026,10:00-11:00
Location: IMS, RS408
Speaker: Xiaoyu Chen, Shanghai Normal University
Abstract: Lusztig defined the a-function for a Coxeter group in 1985, and proposed the famous conjecture P1-P15 in 2004, which will hold for equal parameter case once the positivity of Kazhdan-Lusztig polynomials and the boundedness of of a-function hold. The boundedness conjecture of a-function for finite rank Coxeter groups is one of the four open problems on Hecke algebras, and is of great interest and still open in most cases. We prove that: (1) Each term in the expansion of product of standard bases of Hecke algebra gives rise to a set of reflecting hyperplanes that pairwisely intersect in the interior of Tits cone (intersecting subset), (2) The cardinality of intersecting subsets is bounded. As a consequence, we prove that a-function is bounded for any Coxeter group of finite rank. This work is joint with Hongsheng Hu.