Palindromic Poincaré polynomials in Type
arXiv:2607.07659
summary
The paper classifies all palindromic Poincaré polynomials for Coxeter groups of type Bₙ and shows that every lower Bruhat interval, and consequently every Poincaré and Kazhdan–Lusztig polynomial, from type Aₙ also appears in type Bₙ.
Abstract
We completely describe the set of all palindromic Poincaré polynomials in type . Additionally, we show that all lower Bruhat intervals in type occur in type . As a consequence, all Poincaré polynomials and all Kazhdan--Lusztig polynomials of type occur in type .
30 pages. Substantially revised Section 6. Minor corrections and expository improvements throughout
Topics & keywords
#palindromic polynomials#poincaré polynomials#bruhat order#type b Coxeter groups#kazhdan-lusztig polynomials#type a intervalstype B_ntype A_nBruhat intervalsKazhdan-LusztigPoincaré polynomialpalindromic