English

A Lie-theoretic construction of spherical symplectic reflection algebras

Quantum Algebra 2010-12-15 v3 Representation Theory

Abstract

We propose a construction of the spherical subalgebra of a symplectic reflection algebra of an arbitrary rank corresponding to a star-shaped affine Dynkin diagram. Namely, it is obtained from the universal enveloping algebra of a certain semi-simple Lie algebra by the process of quantum Hamiltonian reduction. As an application, we propose a construction of finite-dimensional representations of the spherical subalgebra.

Keywords

Cite

@article{arxiv.0801.2339,
  title  = {A Lie-theoretic construction of spherical symplectic reflection algebras},
  author = {P. Etingof and S. Loktev and A. Oblomkov and L. Rybnikov},
  journal= {arXiv preprint arXiv:0801.2339},
  year   = {2010}
}

Comments

LaTeX, 17 pages, 2 figures. Final version

R2 v1 2026-06-21T10:03:10.874Z