Conjectures about certain parabolic Kazhdan--Lusztig polynomials

Abstract

Irreducibility results for parabolic induction of representations of the general linear group over a local non-archimedean field can be formulated in terms of Kazhdan--Lusztig polynomials of type $A$. Spurred by these results and some computer calculations, we conjecture that certain alternating sums of Kazhdan--Lusztig polynomials known as parabolic Kazhdan--Lusztig polynomials satisfy properties analogous to those of the ordinary ones.

final version

References in corpus (3)

• Geometric conditions for $\square$-irreducibility of certain representations of the general linear group over a non-archimedean local field
• A tightness property of relatively smooth permutations
• The anti-spherical category

Cited by in corpus (1)

• Geometric conditions for $\square$-irreducibility of certain representations of the general linear group over a non-archimedean local field