Irregular Wakimoto modules and the Casimir connection

Details Irregular Wakimoto modules and the Casimir connection Irregular Wakimoto modules and the Casimir connection

2008-12-24

arxiv.org/abs/0812.4472v3

Selecta Mathematica, Vol. 16(2), July 2010

Mathematics

Representation Theory

Final version, available at Springerlink.com

Scientific paper

10.1007/s00029-010-0019-x

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.

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