Classification of Harish-Chandra Modules for Current Algebras

Lau, Michael

doi:10.1090/proc/13834

Classification of Harish-Chandra Modules for Current Algebras
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by Michael Lau PDF

Proc. Amer. Math. Soc. 146 (2018), 1015-1029 Request permission

Abstract:

For any reductive Lie algebra $\mathfrak {g}$ and commutative, associative, unital algebra $S$, we give a complete classification of the simple weight modules of $\mathfrak {g}\otimes S$ with finite weight multiplicities. In particular, any such module is parabolically induced from a simple admissible module for a Levi subalgebra. Conversely, all modules obtained in this way have finite weight multiplicities. These modules are isomorphic to tensor products of evaluation modules at distinct maximal ideals of $S$. Our results also classify simple Harish-Chandra modules up to isomorphism for all central extensions of current algebras.

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