Harish-Chandra homomorphisms and symplectic reflection algebras for wreath-products

2005/11/20 by Pavel Etingof, Wee Liang Gan, Etingof, Pavel +5
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.math/0511489

openalex publication_date 2005/11/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The main result of the paper is a natural construction of the spherical subalgebra in a symplectic reflection algebra associated with a wreath-product in terms of quantum hamiltonian reduction of an algebra of differential operators on a representation space of an extended Dynkin quiver. The existence of such a construction has been conjectured in [EG]. We also present a new approach to reflection functors and shift functors for generalized preprojective algebras and symplectic reflection algebras associated with wreath-products.

Citations

• Algebras Generated by Elements with Given Spectrum and Scalar Sum and Kleinian Singularities
• Decomposition of Marsden–Weinstein Reductions for Representations of Quivers
• Quantization of minimal resolutions of Kleinian singularities

Related

• Symplectic reflection algebras, Calogero-Moser space, and deformed Harish-Chandra homomorphism
• Symplectic reflection algebras and affine Lie algebras
• Symplectic reflection algebras
• Reflection functors and symplectic reflection algebras for wreath products
• Representations of symplectic reflection algebras and resolutions of deformations of symplectic quotient singularities