Finite-dimensional representations of hyper multicurrent and multiloop algebras

2019/05/12 by Angelo Bianchi, Bianchi, Angelo, Samuel Chamberlin +1 · 2 citations
Mathematics · #14L17 #17B10 #17B65 #FOS: Mathematics #Representation Theory (math.RT) #math.RT #msc:14L17 #msc:17B10 #msc:17B65

paper · pdf · doi:10.48550/arxiv.1905.04630

The paper was revised for publication, some details were added and few typos were fixed

arxiv created 2020/02/05 · arxiv updated 2020/02/07

Abstract

We investigate the categories of finite-dimensional representations of multicurrent and multiloop hyperalgebras in positive characteristic, i.e., the hyperalgebras associated to the multicurrent algebras \mathfrak g⊗ℂ[t₁,…,t_n] and to the multiloop algebras \mathfrak g⊗ℂ[t₁^±1,…,t_n^{± 1}], where \mathfrak g is any finite-dimensional complex simple Lie algebra. The main results are the construction of the universal finite-dimensional highest-weight modules and a classification of irreducible modules in each category. In the characteristic zero setting we also provide a relationship between them.

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