BRST cohomologies for symplectic reflection algebras and quantizations of hypertoric varieties

Abstract

We study algebras constructed by quantum Hamiltonian reduction associated with symplectic quotients of symplectic vector spaces, including deformed preprojective algebras, symplectic reflection algebras (rational Cherednik algebras), and quantization of hypertoric varieties introduced by Musson and Van den Bergh. We determine BRST cohomologies associated with these quantum Hamiltonian reductions. To compute these BRST cohomologies, we make use of method of deformation quantization (DQ-algebras) and F-action studied in [Kashiwara-Rouquier], and in [Gordon-Losev].