Vertex Operators, Grassmannians, and Hilbert Schemes |
| |
Authors: | Erik Carlsson |
| |
Institution: | 1. Department of Mathematics, Northwestern University, 2033 Sheridan Road, Evanston, IL, 60208, USA
|
| |
Abstract: | We approximate the infinite Grassmannian by finite-dimensional cutoffs, and define a family of fermionic vertex operators
as the limit of geometric correspondences on the equivariant cohomology groups, with respect to a one-dimensional torus action.
We prove that in the localization basis, these are the well-known fermionic vertex operators on the infinite wedge representation.
Furthermore, the boson-fermion correspondence, locality, and intertwining properties with the Virasoro algebra are the limits
of relations on the finite-dimensional cutoff spaces, which are true for geometric reasons. We then show that these operators
are also, almost by definition, the vertex operators defined by Okounkov and the author in Carlsson and Okounkov ( math.AG], 2009), on the equivariant cohomology groups of the Hilbert scheme of points on
\mathbb C2{\mathbb C^2} , with respect to a special torus action. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|