Multiplicative McKay correspondence in the symplectic case

TL;DR

This paper discusses the proof of Y. Ruan's conjecture on orbifold cohomology multiplication for symplectic quotient singularities, providing an informal overview of the key ideas and results.

Contribution

It offers an accessible summary and explanation of the proof of Ruan's conjecture in the symplectic case, clarifying complex algebraic structures involved.

Findings

Proof of Y. Ruan's conjecture on orbifold cohomology multiplication

Clarification of symplectic quotient singularities

Connections to the multiplicative McKay correspondence

Abstract

This is a write-up of my talk at the Conference on algebraic structures in Montreal, July 2003. I try to give a brief informal introduction to the proof of Y. Ruan's conjecture on orbifold cohomology multiplication for symplectic quotient singularities given in V. Ginzburg and D. Kaledin, math.AG/0212279. Version 2: minor changes, added some references.