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.
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