Rational Cherednik algebras of G(ℓ,p,n) from the Coulomb perspective

We prove a number of results on the structure and representation theory of the rational Cherednik algebra of the imprimitive reflection group G(ℓ,p,n). In particular, we: (1) show a relationship to the Coulomb branch construction of Braverman, Finkelberg, and Nakajima, and 3-dimensional quantum fiel...

Full description

Saved in:
Bibliographic Details
Published in:Advances in mathematics (New York. 1965) 2023-11, Vol.433, p.109295, Article 109295
Main Authors: LePage, Elise, Webster, Ben
Format: Article
Language:English
Subjects:
Cherednik algebra
Complex reflection group
Coulomb branch
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We prove a number of results on the structure and representation theory of the rational Cherednik algebra of the imprimitive reflection group G(ℓ,p,n). In particular, we: (1) show a relationship to the Coulomb branch construction of Braverman, Finkelberg, and Nakajima, and 3-dimensional quantum field theory; (2) show that the spherical Cherednik algebra carries the structure of a principal Galois order; (3) construct a graded lift of category O and the larger category of Dunkl-Opdam modules, whose simple modules have the properties of a dual canonical basis and (4) give the first classification of simple Dunkl-Opdam modules for the rational Cherednik algebra of the imprimitive reflection group G(ℓ,p,n).
ISSN:0001-8708
1090-2082
DOI:10.1016/j.aim.2023.109295