Transformation Groups 20(2) 437-461 2015 [Refereed]

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 quantizat...

Pacific Journal of Mathematics 260(1) 89-127 Sep 2012 [Refereed]

Based on a construction by Kashiwara and Rouquier, we present an ana- logue of the Beilinson–Bernstein localization theorem for hypertoric vari- eties. In this case, sheaves of differential operators are replaced by sheaves of W-algebras. As a spe...

Based on the methods developed in [Kashiwara-Rouquier], we consider
microlocalization of the rational Cherednik algebra of type . Our goal
is to construct the irreducible modules and standard modules of the rational
Cherednik algebra by us...

We introduce the notion of an asymptotic algebra of chiral differential operators. We then construct, via a chiral Hamiltonian reduction, one such algebra over a resolution of the intersection of the Slodowy slice with the nilpotent cone. We compu...

Characteristic cycles of standard modules for the rational Cherednik algebra of type

Kuwabara, Toshiro

J. Math. Kyoto Univ. 48(no. 1) 167-217 2008 [Refereed]

Constructing subregular W-algebras with microlocal differential operators

Toshiro Kuwabara

Workshop on Finite Groups, VOA, and algebraic combinatorics 22 Mar 2016

Using chiral analogue of microlocal differential operators, we construct vertex algebras associated with some symplectic manifolds. Such a construction includes a new construction of the affine W-algebra of subregular type A. Moreover, from the co...

In this talk, we discuss sheaves of (h-adic) vertex algebras on symplectic manifolds, which give quantization of vertex Poisson algebras of their Jet bundles. On each formal coordinate, these sheaves are isomorphic to the vertex algebra of a forma...

BRST cohomologies for rational Cherednik algebras[Invited]

Toshiro Kuwabara

RIMS Project 2014 Geometric Representation Theory 28 Jul 2014

BRST cohomologies for rational Cherednik algebras[Invited]

Toshiro Kuwabara

Shanghai Workshop on Representation Theory 2013 5 Dec 2013 East China Normal University; Tongji University; Osaka University

Quantization of Kleinian singularities can be realized as two different quantum Hamilto- nian reductions. They are known as rational Cherednik algebras (symplectic reflection algebras) and finite W-algebras. Losev showed that these two quantizatio...

Workshop “Integrable Systems, Random Matrices, Algebraic Geometry and Geometric Invariants” 21 Feb 2012

The affine W -algebras are vertex algebras which generalize the Virasoro algebra and are constructed by Drinfeld-Sokolov reduction of affine vertex algebras. We construct a sheaf of vertex algebras on the arc space (the infinite-Jet sheme) of the ...

Localization of affine W-algebras at critical level

Toshiro Kuwabara

Japan Mathematical Society Conference 28 Sep 2011 Japan Mathematical Society

Localization of affine W-algebras at critical level

Toshiro Kuwabara

Seminar in Lie Theory of NTU 21 Aug 2011 National Taiwan University

HIM Trimester Program on On the Interaction of Representation Theory with Geometry and Combinatorics 18 Apr 2011 Hausdorff Research Institute for Mathematics

On localization of quantized hypertoric algebras and microlocal analysis

Toshiro Kuwabara

Oberseminar 10 Mar 2011 Max-Planck Institute for Mathematics

Starting from a well-known and easy example of the Beilinson-Bernstein
correspondence for the case of U(sl_2), I will explain how we consider
``localization'' for some noncommutative algebras, which I will call quantized
hypertoric algebras in t...

Introduction to Cherednik algebras 13 Jan 2011 Graduate School of Mathematics, Nagoya Univ.

In this talk, I will survey the new scheme for localization of some noncommutative algebras which is first established by Kashiwara and Rouquier. Both the rational Cherednik algebras and the finite W-algebras are algebras constructed as quantizati...

Microlocal Analysis and Representation Theory of the Rational Cherednik Algebras[Invited]

Toshiro Kuwabara

Mini Symposium on Representation Theory Dec 2010 Prof. Kang, Seok-Jin

Some noncommutative algebras and their representation theory are closely related to
geometry of some important manifolds or varieties, such as flag varieties or quiver
varieties. These connections sometimes imply ``localization'' of the noncommu...

Representation Theory of Algebraic Groups and Quantum Groups '10 Aug 2010 Graduate School of Mathematics, Nagoya University

We will discuss the geometric representation theory for the rational Cherednik algebra of type Z/lZ.
The rational Cherednik algebra of type Z/lZ is defined as a quantization of the Kleinian singularities of type A. This algebra is also called the...

A rational Cherednik algebra as a noncommutative deformation of a quiver variety

Toshiro Kuwabara

Russia-Japan School of Young Mathematicians Jan 2009 GCOE Program, Math. Dept. and RIMS, Kyoto University

Characteristic cycles of standard modules for the rational Cherednik algebra of type

Toshiro Kuwabara

Workshop on Algebras in Lie theory Sep 2008 RIMS, Kyoto Univ.

The rational Cherednik algebra as a noncommutative deformation of the quiver variety[Invited]

Toshiro Kuwabara

A workshop on micro-local analysis on symplectic manifolds Sep 2008 IPMU, University of Tokyo

Symplectic reflection algebras and quiver varieties

Toshiro Kuwabara

Seoul National University and Kyoto University, Workshop for Young Mathematicians Feb 2006 Math. Dept of Seoul National Univ., Math. Dept. and RIMS of Kyoto Univ.

Symplectic reflection algebras and quiver varieties

Toshiro Kuwabara

Infinite Analysis Seminar, Japan-Russia International Project Mar 2005

Symmmetric coinvariant algebras and local Weyl modules at a double point

Toshiro Kuwabara

Quantum Integrable Systems and Infinite Dimensional Algebras Feb 2004 RIMS, Kyoto Univ.