Dirac cohomology of highest weight modules
type: Item
instance of: scholarly article
title: Dirac cohomology of highest weight modules
zbMATH Open document ID: 1257.22012
author: Wei Xiao
author: Jing-Song Huang
published in: Selecta Mathematica. New Series
publication date: 2012-12-19T00:00:00Z
review text: In this paper the authors explicitly describe the Dirac cohomology of simple highest weight modules over a finite dimensional complex semi-simple Lie algebra. The answer is given in terms of relative Kazhdan-Lusztig polynomials.
reviewed by: Volodymyr Mazorchuk
Mathematics Subject Classification ID: 22E46
Mathematics Subject Classification ID: 22E47
zbMATH DE Number: 6116925
zbMATH Keywords: Dirac cohomology
zbMATH Keywords: highest weight module
zbMATH Keywords: category O
zbMATH Keywords: nilpotent Lie algebra
MaRDI profile type: Publication
full work available at URL: s00029-011-0085-8
OpenAlex ID: W1963877759
cites work: Category of \(\mathfrak g\) modules
cites work: Koszul Duality Patterns in Representation Theory
cites work: Kostant Modules in Blocks of Category 𝒪S
cites work: The Kazhdan-Lusztig conjecture for generalized Verma modules
cites work: Q4112093
cites work: On some geometric aspects of Bruhat orderings. II: The parabolic analogue of Kazhdan-Lusztig polynomials
cites work: Jacquet modules and Dirac cohomology
cites work: Analogues of Kostant's -cohomology formulas for unitary highest weight modules.
cites work: Categories of highest weight modules: applications to classical Hermitian symmetric pairs
cites work: Dirac cohomology, unitary representations and a proof of a conjecture of Vogan
cites work: Dirac cohomology of some Harish-Chandra modules
cites work: Dirac operators and Lie algebra cohomology
cites work: Q3518603
cites work: Singular blocks of the category \({\mathcal O}\)
cites work: A cubic Dirac operator and the emergence of Euler number multiplets of representations for equal rank subgroups
cites work: A generalization of the Bott-Weil theorem and Euler number multiplets of representations
cites work: Q4437890
cites work: Vanishing theorems for Lie algebra cohomology and the cohomology of discrete subgroups of semisimple Lie groups
cites work: \(\mathfrak n\)-cohomology of simple highest weight modules on walls and purity
cites work: Kategorie O , Perverse Garben Und Moduln Uber Den Koinvariantez Zur Weylgruppe
DOI: 10.1007/S00029-011-0085-8
Recommended article: Dirac cohomology and orthogonality relations for weight modules
Recommended article: Higher Dirac cohomology of modules with generalized infinitesimal character
Recommended article: Dirac cohomology of some Harish-Chandra modules
Recommended article: Dirac cohomology in representation theory
Recommended article: Jacquet modules and Dirac cohomology
Recommended article: Dirac cohomology and character lifting
Recommended article: Dirac cohomology of cohomologically induced modules for reductive Lie groups
Recommended article: Higher cohomologies of modules
Recommended article: Dirac cohomology and Dirac induction
Recommended article: The Dirac cohomology of a finite dimensional representation
description: scientific article; zbMATH DE number 6116925