Finite dimensional representations of rational Cherednik algebras
Yuri Berest, Pavel Etingof, Victor Ginzburg
TL;DR
This paper classifies all finite-dimensional irreducible representations of rational Cherednik algebras of type A, explores their character formulas, and discusses connections to affine flag manifolds and Hilbert schemes.
Contribution
It provides a complete classification and character formulas for type A, and extends some results to other types, linking algebraic and geometric perspectives.
Findings
Complete classification for type A representations
Character formulas for irreducible representations
Connections to affine flag manifolds and Hilbert schemes
Abstract
A complete classification and character formulas for finite-dimensional irreducible representations of the rational Cherednik algebra of type A is given. Less complete results for other types are obtained. Links to the geometry of affine flag manifolds and Hilbert schemes are discussed.
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Advanced Algebra and Geometry