Palindromic Poincaré polynomials in Type $B$

Gaston Burrull

Palindromic Poincaré polynomials in Type $B$

Combinatorics 2026-07-08 v1 Representation Theory

Authors: Gaston Burrull

Abstract

We completely describe the set of all palindromic Poincar\'e polynomials in type $B_n$ . Additionally, we show that all lower Bruhat intervals in type $A_n$ occur in type $B_n$ . As a consequence, all Poincar\'e polynomials $P_w(q)$ and all Kazhdan--Lusztig polynomials $P_{x,y}(q)$ of type $A_n$ occur in type $B_n$ .

Cite

@article{arxiv.2607.07659,
  title  = {Palindromic Poincaré polynomials in Type $B$},
  author = {Gaston Burrull},
  journal= {arXiv preprint arXiv:2607.07659},
  year   = {2026}
}

Comments

23 pages