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arXiv · 0812.4472

Irregular Wakimoto modules and the Casimir connection

Roman M. Fedorov
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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.

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BibTeXRIS

Roman M. Fedorov. 2008-12-24. Irregular Wakimoto modules and the Casimir connection. https://doi.org/10.1007/s00029-010-0019-x

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