Search engine for discovering works of Art, research articles, and books related to Art and Culture
Javascript must be enabled to continue!
Monotonicity of inverse Kazhdan-Lusztig polynomials
View through CrossRef
For arbitrary Coxeter systems, we prove that inverse Kazhdan-Lusztig polynomials satisfy a monotonicity property. This follows from the validity of Soergel’s conjecture and the existence of injective morphisms between Rouquier complexes in the mixed perverse Hecke category. The monotonicity property is generalised to parabolic Kazhdan-Lusztig polynomials.
American Mathematical Society (AMS)
Title: Monotonicity of inverse Kazhdan-Lusztig polynomials
Description:
For arbitrary Coxeter systems, we prove that inverse Kazhdan-Lusztig polynomials satisfy a monotonicity property.
This follows from the validity of Soergel’s conjecture and the existence of injective morphisms between Rouquier complexes in the mixed perverse Hecke category.
The monotonicity property is generalised to parabolic Kazhdan-Lusztig polynomials.
Related Results
Matroid relaxations and Kazhdan–Lusztig non-degeneracy
Matroid relaxations and Kazhdan–Lusztig non-degeneracy
In this paper we study the interplay between the operation of circuit-hyperplane relaxation and the Kazhdan–Lusztig theory of matroids. We obtain a family of polynomials, not depen...
Generic Algebras and Kazhdan-Lusztig Theory for Monomial Groups
Generic Algebras and Kazhdan-Lusztig Theory for Monomial Groups
The Iwahori-Hecke algebras of Coxeter groups play a central role in the study of representations of semisimple Lie-type groups. An important tool is the combinatorial approach to r...
A Gröbner basis for Kazhdan-Lusztig ideals
A Gröbner basis for Kazhdan-Lusztig ideals
{\it Kazhdan-Lusztig ideals}, a family of generalized determinantal ideals
investigated in [Woo-Yong~'08], provide an explicit choice of coordinates
and equations encoding a neig...
On the torsion part in the cohomology of Deligne-Lusztig varieties
On the torsion part in the cohomology of Deligne-Lusztig varieties
Sur la partie de torsion dans la cohomologie des variétés Deligne–Lusztig
Dans cette thèse, nous étudions quelques méthodes géométriques dues à Deligne et Lusztig p...
Evaluating Manifest Monotonicity Using Bayes Factors
Evaluating Manifest Monotonicity Using Bayes Factors
The assumption of latent monotonicity in item response theory models for dichotomous data cannot be evaluated directly, but observable consequences such as manifest monotonicity fa...
On Convolved Fibonacci Polynomials
On Convolved Fibonacci Polynomials
This work delves deeply into convolved Fibonacci polynomials (CFPs) that are considered generalizations of the standard Fibonacci polynomials. We present new formulas for these pol...
Novel Formulas of Schröder Polynomials and Their Related Numbers
Novel Formulas of Schröder Polynomials and Their Related Numbers
This paper explores the Schröder polynomials, a class of polynomials that produce the famous Schröder numbers when x=1. The three-term recurrence relation and the inversion formula...
Some Orthogonal Combinations of Legendre Polynomials
Some Orthogonal Combinations of Legendre Polynomials
The principle objective of this article is to introduce and investigate a type of orthogonal polynomials that are written as combinations of Legendre polynomials. This kind of poly...