## 23 Citations

Finite dimensional Hopf actions on algebraic quantizations

- Mathematics
- 2016

Let k be an algebraically closed field of characteristic zero. In joint work with J. Cuadra [arxiv.org/abs/1409.1644, arxiv.org/abs/1509.01165], we showed that a semisimple Hopf action on a Weyl…

Poisson traces, D-modules, and symplectic resolutions

- MathematicsLetters in mathematical physics
- 2018

The theory of Poisson traces (or zeroth Poisson homology) developed by the authors is surveyed, to understand this subtle invariant of (singular) Poisson varieties, conditions for it to be finite-dimensional, its relationship to the geometry and topology of symplectic resolutions, and its applications to quantizations.

Derived Equivalences for Symplectic Reflection Algebras

- MathematicsInternational Mathematics Research Notices
- 2019

In this paper we study derived equivalences for symplectic reflection algebras. We establish a version of the derived localization theorem between categories of modules over these algebras and…

Bernstein's inequality and holonomicity for certain singular rings

- Mathematics
- 2021

. In this manuscript, we prove the Bernstein inequality and develop the theory of holonomic D -modules for rings of invariants of ﬁnite groups in characteristic zero, and for strongly F -regular…

Semisimplicity of the category of admissible D-modules

- MathematicsKyoto Journal of Mathematics
- 2017

Using a representation theoretic parameterization for the orbits in the enhanced cyclic nilpotent cone, derived by the authors in a previous article, we compute the fundamental group of these orbits.…

Non-vanishing of geometric Whittaker coefficients for reductive groups

- Mathematics
- 2022

We prove that cuspidal automorphic D-modules have non-vanishing Whittaker coefficients, generalizing known results in the geometric Langlands program from GLn to general reductive groups. The key…

An investigation into Lie algebra representations obtained from regular holonomic D-modules

- Mathematics
- 2021

Beilinson–Bernstein localisation [BB81] relates representations of a Lie algebra g to certain D-modules on the flag variety of g. In [Rom21], examples of sl2-representations which correspond to…

Affine Springer Fibers, Procesi bundles, and Cherednik algebras

- Mathematics
- 2021

Let g be a semisimple Lie algebra, t its Cartan subalgebra and W the Weyl group. The goal of this paper is to prove an isomorphism between suitable completions of the equivariant Borel-Moore homology…

Quantum Hamiltonian Reduction for Polar Representations

- Mathematics
- 2021

Let G be a reductive complex Lie group with Lie algebra g and suppose that V is a polar G-representation. We prove the existence of a radial parts map rad : D(V ) → Aκ from the G-invariant…

## References

SHOWING 1-10 OF 22 REFERENCES

Quantizations of conical symplectic resolutions I: local and global structure

- Mathematics
- 2012

We re-examine some topics in representation theory of Lie algebras and Springer theory in a more general context, viewing the universal enveloping algebra as an example of the section ring of a…

Cherednik algebras and differential operators on quasi-invariants

- Mathematics
- 2001

We develop representation theory of the rational Cherednik algebra H associated to a finite Coxeter group W in a vector space h. It is applied to show that, for integral values of parameter `c', the…

On primitive ideals

- Mathematics
- 2002

AbstractWe extend two well-known results on primitive ideals in enveloping
algebras of semisimple Lie algebras, the
Irreducibility
theorem for associated varieties and
Duflo theorem
on primitive…

Quantized symplectic actions and W -algebras

- Mathematics
- 2007

With a nilpotent element in a semisimple Lie algebra g one associates a finitely generated associative algebra W called a W-algebra of finite type. This algebra is obtained from the universal…

On the category 𝒪 for rational Cherednik algebras

- Mathematics
- 2002

Abstract We study the category 𝒪 of representations of the rational Cherednik algebra AW attached to a complex reflection group W. We construct an exact functor, called Knizhnik-Zamolodchikov…

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

- Mathematics
- 2005

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…

Poisson Traces and D-Modules on Poisson Varieties

- Mathematics
- 2009

To every Poisson algebraic variety X over an algebraically closed field of characteristic zero, we canonically attach a right D-module M(X) on X. If X is affine, solutions of M(X) in the space of…

Fundamental groups of symplectic singularities

- Mathematics
- 2013

Let (X, \omega) be an affine symplectic variety. Assume that X has a C^*-action with positive weights and \omega is homogeneous with respect to the C^*-action. We prove that the algebraic fundamental…

Etingof’s conjecture for quantized quiver varieties

- Mathematics
- 2013

We compute the number of finite dimensional irreducible modules for the algebras quantizing Nakajima quiver varieties. We get a lower bound for all quivers and vectors of framing and provide an exact…