Duke Mathematical Journal

Finite-dimensional representations of W-algebras

Ivan Losev

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W-algebras of finite type are certain finitely generated associative algebras closely related to the universal enveloping algebras of semisimple Lie algebras. In this article, we prove a conjecture of Premet that gives an almost complete classification of finite-dimensional irreducible modules for W-algebras. A key ingredient in our proof is a relationship between Harish-Chandra bimodules and bimodules over W-algebras that is also of independent interest.

Article information

Duke Math. J., Volume 159, Number 1 (2011), 99-143.

First available in Project Euclid: 11 July 2011

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 16G99: None of the above, but in this section 17B35: Universal enveloping (super)algebras [See also 16S30]


Losev, Ivan. Finite-dimensional representations of $W$ -algebras. Duke Math. J. 159 (2011), no. 1, 99--143. doi:10.1215/00127094-1384800. https://projecteuclid.org/euclid.dmj/1310416364

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