Endomorphisms of Verma modules for rational Cherednik algebras
type: Item
instance of: scholarly article
title: Endomorphisms of Verma modules for rational Cherednik algebras
zbMATH Open document ID: 1352.16020
published in: Transformation Groups
publication date: 2014-09-04T00:00:00Z
full work available at URL: https://arxiv.org/abs/1312.7524
review text: In this paper, the author studies endomorphisms of Verma modules for rational Cherednik algebras of complex reflection groups, for the special value \(t=0\) of the defining parameter. For this value of the parameter, the rational Cherednik algebra is a finite module over the center of the algebra. The main result of the paper shows that, in many cases, the center of the rational Cherednik algebra surjects onto the endomorphism algebra of a Verma module. In some special cases, it is shown that the endomorphism algebra of a Verma module is a polynomial ring and the Verma module is free over this polynomial ring, of rank equal to the cardinality of the complex reflection group used to define the rational Cherednik algebra. The results of the paper are motivated by their description in the context of derived intersections of Lagrangian subvarieties of the generalized Calogero-Moser spaces.
reviewed by: Volodymyr Mazorchuk
Mathematics Subject Classification ID: 16G99
Mathematics Subject Classification ID: 17B10
Mathematics Subject Classification ID: 20F55
zbMATH DE Number: 6339819
zbMATH Keywords: endomorphism
zbMATH Keywords: Verma module
zbMATH Keywords: rational Cherednik algebra
zbMATH Keywords: center
zbMATH Keywords: Calogero-Moser space
zbMATH Keywords: Lagrangian subvariety
author: Gwyn Bellamy
MaRDI profile type: Publication
OpenAlex ID: W2030948827
arXiv ID: 1312.7524
cites work: A New Algebraic Approach to Microlocalization of Filtered Rings
cites work: Gerstenhaber-Batalin-Vilkoviski structures on coisotropic intersections
cites work: Gerstenhaber and Batalin–Vilkovisky Structures on Lagrangian Intersections
cites work: Cuspidal representations of rational Cherednik algebras at \(t=0\).
cites work: Rational Cherednik algebras and Schubert cells
cites work: Constructibility and duality for simple holonomic modules on complex symplectic manifolds
cites work: A new linear quotient of \(\mathbf C^4\) admitting a symplectic resolution.
cites work: Q4273960
cites work: Q4399851
cites work: Parabolic induction and restriction functors for rational Cherednik algebras.
cites work: Some theorems on actions of algebraic groups
cites work: Self-extensions of Verma modules and differential forms on opers
cites work: The ramification of centres: Lie algebras in positive characteristic and quantised enveloping algebras
cites work: A differential complex for Poisson manifolds
cites work: Q2785535
cites work: Krull Dimension of Modules and Involutive Ideals
cites work: Poisson structures and their normal forms
cites work: Symplectic reflection algebras, Calogero-Moser space, and deformed Harish-Chandra homomorphism.
cites work: Q5308978
cites work: A survey on symplectic singularities and symplectic resolutions
cites work: The Integrability of the Characteristic Variety
cites work: On the category \(\mathcal O\) for rational Cherednik algebras.
cites work: BABY VERMA MODULES FOR RATIONAL CHEREDNIK ALGEBRAS
cites work: Symplectic reflection algebras
cites work: Éléments de géométrie algébrique. I: Le langage des schémas. II: Étude globale élémentaire de quelques classe de morphismes. III: Étude cohomologique des faisceaux cohérents (première partie)
cites work: Q4143433
cites work: Microlocalization of rational Cherednik algebras
cites work: Cyclotomic double affine Hecke algebras and affine parabolic category \(\mathcal O\).
DOI: 10.1007/S00031-014-9281-X
description: scientific article; zbMATH DE number 6339819