BGG reciprocity for current algebras

2013/07/31 by Vyjayanthi Chari, Bogdan Ion · 9 citations
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology #math.CO #math.QA #math.RT #msc:17B10 #msc:17B67

paper · pdf · doi:10.1112/s0010437x14007908

published as Compositio Mathematica 151 (2015) 1265-1287 · 23 pg, corrections to Lemma 2.14

arxiv created 2014/08/20 · arxiv updated 2015/07/29

Abstract

It was conjectured by Bennett, Chari, and Manning that a BGG-type reciprocity holds for the category of graded representations with finite-dimensional graded components for the current algebra associated to a simple Lie algebra. We associate a current algebra to any indecomposable affine Lie algebra and show that, in this generality, the BGG reciprocity is true for the corresponding category of representations.

Cited by

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• Trace and categorical sl(n) representations
• Macdonald Polynomials and BGG reciprocity for current algebras
• Positive level, negative level and level zero
• Macdonald Polynomials and level two Demazure modules for affine \mathfraksl_n+1
• A Weyl Module Stratification of Integrable Representations (with an appendix by Ryosuke Kodera)
• Peter-Weyl, Howe and Schur-Weyl theorems for current groups
• Graded representations of current Lie superalgebras \mathfraksl(1|2)[t]
• Symmetric functions and Springer representations
• Generalized Weyl modules for twisted current algebras

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