Microlocalization of rational Cherednik algebras

By Masaki Kashiwara, Raphaël Rouquier. 2007

78 citations recorded by the source corpus.

We construct a microlocalization of the rational Cherednik algebras H of type Sn. This is achieved by a quantization of the Hilbert scheme Hilb C2 of n points in C2. We then prove the equivalence of the category of H -modules and that of modules over its microlocalization under certain conditions on the parameter.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/5742ec420432c0d0a0e185cf1c85e6db2c928724

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. Andrei Neguct
2. T. Nevins
3. Kevin McGerty
4. E. Gorsky
5. I. Gordon
6. I. Losev

In Geometry and Topology

1. Andrei Neguct
2. T. Nevins
3. Kevin McGerty
4. E. Gorsky
5. I. Losev
6. I. Gordon

In Mathematical Physics

1. Andrei Neguct
2. T. Nevins
3. Kevin McGerty
4. E. Gorsky
5. I. Losev
6. I. Gordon

Citations in the corpus

• Refined knot invariants and Hilbert schemes (2013, background): “Kashiwara and Rouquier ([44]) have constructed a quantization of the Hilbert scheme depending on a parameter c, such that the category of coherent sheaves over this quantization is equivalent to the category of representations of Hc.”
• Derived equivalence for quantum symplectic resolutions (2011, background): “It also establishes the derived version of microlocalization of rational Cherednik algebras of type A [39] and hypertoric enveloping algebras [6] and yields a new derived microlocalization theorem relating cyclotomic rational Cherednik algebras with quantizations of the Hilbert schemes ( ̃ C2/ ) [n]”