Classification of simple W_n-modules with finite-dimensional weight spaces

2013/04/19 by Billig, Yuly, Futorny, Vyacheslav
#17B10 #17B66 #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1304.5458

Abstract

We classify all simple W_n-modules with finite-dimensional weight spaces. Every such module is either of a highest weight type or is a quotient of a module of tensor fields on a torus, which was conjectured by Eswara Rao. This generalizes the classical result of Mathieu on simple weight modules for the Virasoro algebra. In our proof of the classification we construct a functor from the category of cuspidal W_n-modules to the category of W_n-modules with a compatible action of the algebra of functions on a torus. We also present a new identity for certain quadratic elements in the universal enveloping algebra of W₁, which provides important information about cuspidal W₁-modules.

Related

• A family of new simple modules over the Schrödinger-Virasoro algebra
• Classification of simple weight modules for the Neveu-Schwarz algebra with a finite-dimensional weight space
• Simple Modules Over the Higher Rank Super-Virasoro Algebras
• Simple weight modules with finite-dimensional weight spaces over Witt superalgebras
• New simple modules for the W-algebra W(2,2)