We develop representation theory of the rational Cherednik algebra \rmH\sbc associated to
a finite Coxeter group W in a vector space h, and a parameter" c." We use it to show that, for …

The F-signature of a local ring of prime characteristic is a numerical invariant that detects
many interesting properties. For example, this invariant detects (non) singularity and strong …

Ring theory from symplectic geometry ’ Page 1 JOURNAL OF PURE AND APPLIED ALGEBRA
Journal of Pure and Applied Algebra 125 (1998) 155-190 Ring theory from symplectic geometry …

Let X be an affine complex algebraic variety, and let T>(X) denote the (non-commutative)
algebra of algebraic differential operators on X. Then T>(X) has a filtration {^(X)} by order of …

The aim of this paper is to study the rings of differential operators on classical rings of
invariants. Though the varieties will often be singular, we will prove that the corresponding …

We introduce quasi-invariant polynomials for an arbitrary finite complex reflection group W.
Unlike in the Coxeter case, the space of quasi-invariants of a given multiplicity is not, in …

We prove that the algebra of integro-differential operators on a polynomial algebra is a
prime, central, catenary, self-dual, non-Noetherian algebra of classical Krull dimension n …

This paper investigates the existence and properties of a Bernstein–Sato functional equation
in nonregular settings. In particular, we construct D-modules in which such formal equations …

Let $ A= A (k) $ be the first Weyl algebra over an infinite field $ k $, let $ P $ be any
noncyclic, projective right ideal of $ A $ and set $ S=\operatorname {End}(P) $. We prove …

Noncommutative Deformation Theory is aimed at mathematicians and physicists studying
the local structure of moduli spaces in algebraic geometry. This book introduces a general …