16 research outputs found
Kazhdan-Lusztig polynomials of matroids under deletion
We present a formula which relates the Kazhdan-Lusztig polynomial of a
matroid , as defined by Elias, Proudfoot and Wakefield, to the
Kazhdan--Lusztig polynomials of the matroid obtained by deleting an element,
and various contractions and localizations of . We give a number of
applications of our formula to Kazhdan--Lusztig polynomials of graphic
matroids, including a simple formula for the Kazhdan--Lusztig polynomial of a
parallel connection graph.Comment: 21 pages, two figures. Minor updates and correction
Equivariant Kazhdan–Lusztig polynomials of -niform matroids
We introduce -analogues of uniform matroids, which we call -niform
matroids. While uniform matroids admit actions of symmetric groups, -niform
matroids admit actions of finite general linear groups. We show that the
equivariant Kazhdan-Lusztig polynomial of a -niform matroid is the unipotent
-analogue of the equivariant Kazhdan-Lusztig polynomial of the corresponding
uniform matroid, thus providing evidence for the positivity conjecture for
equivariant Kazhdan-Lusztig polynomials.Comment: References added; typos correcte