Palindromic Poincaré polynomials in $B_n$

Abstract

We describe the set of palindromic Poincaré polynomials in $B_n$. As a key ingredient in this classification, we prove that $A_n$ embeds into $B_n$ as a lower interval in Bruhat order. Consequently, all Poincare polynomials $P_w(q)$ and all Kazhdan--Lusztig polynomials $P_{x,y}(q)$ of $A_n$ occur in $B_n$.

arXiv comment27 pages. Numerous expository improvements and streamlined arguments. The main change is the use of Lakshmibai's characterization of Kempf elements, which substantially shortens Section 5