Factorization in generalized Calogero-Moser spaces

TL;DR

This paper proves a factorization property of the Etingof-Ginzburg sheaf on generalized Calogero-Moser spaces, confirming a conjecture for symmetric groups and advancing understanding of these algebraic structures.

Contribution

It establishes a new factorization result for the Etingof-Ginzburg sheaf on generalized Calogero-Moser spaces, confirming a key conjecture for symmetric groups.

Findings

Confirmed the conjecture of Etingof and Ginzburg for W = S_n.

Established a factorization of the Etingof-Ginzburg sheaf.

Connected recent constructions to the structure of Calogero-Moser spaces.

Abstract

Using a recent construction of Bezrukavnikov and Etingof we prove that there is a factorization of the Etingof-Ginzburg sheaf on the generalized Calogero-Moser space associated to a complex reflection group. In the case W = S_n, this confirms a conjecture of Etingof and Ginzburg.