Rational Cherednik algebras and categorification
Ivan Losev

TL;DR
This survey reviews how Kac-Moody and Heisenberg algebra actions on categories of rational Cherednik algebras facilitate solving key representation theory problems like classifying finite-dimensional irreducibles and computing their characters.
Contribution
It introduces a categorification approach using algebra actions to address fundamental representation theoretic questions for rational Cherednik algebras.
Findings
Classification of finite-dimensional irreducible representations
Explicit computation of characters for irreducibles
Application of algebra actions to solve representation problems
Abstract
In this survey article we review Kac-Moody and Heisenberg algebra actions on the categories of the rational Cherednik algebras associated to groups . Using these actions we solve basic representation theoretic problems for these categories such as the classification of finite dimensional irreducible representations and computation of characters of the irreducibles.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Advanced Algebra and Geometry
