Irregular Wakimoto modules and the Casimir connection
Representation Theory
2010-08-17 v3 Algebraic Geometry
Quantum Algebra
Abstract
We study some non-highest weight modules over an affine Kac-Moody algebra at non-critical level. Roughly speaking, these modules are non-commutative localizations of some non-highest weight "vacuum" modules. Using free field realization, we embed some rings of differential operators in endomorphism rings of our modules. These rings of differential operators act on a localization of the space of coinvariants of any module over the Kac-Moody algebra with respect to a certain level subalgebra. In a particular case this action is identified with the Casimir connection.
Cite
@article{arxiv.0812.4472,
title = {Irregular Wakimoto modules and the Casimir connection},
author = {Roman M. Fedorov},
journal= {arXiv preprint arXiv:0812.4472},
year = {2010}
}
Comments
Final version, available at Springerlink.com