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BGG reciprocity for current algebras

Part of: Lie algebras and Lie superalgebras Basic hypergeometric functions

Published online by Cambridge University Press:  09 February 2015

Vyjayanthi Chari  and
Bogdan Ion
Vyjayanthi Chari
Affiliation:
Department of Mathematics, University of California, Riverside, CA 92521, USA email chari@math.ucr.edu
Bogdan Ion
Affiliation:
Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260, USA email bion@pitt.edu Algebra and Number Theory Research Center, Faculty of Mathematics and Computer Science, University of Bucharest, 14 Academiei St., Bucharest, Romania
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Abstract

In Bennett et al. [BGG reciprocity for current algebras, Adv. Math. 231 (2012), 276–305] it was conjectured 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.

Keywords

current algebraWeyl moduleMacdonald polynomial

MSC classification

Primary: 17B10: Representations, algebraic theory (weights) 17B67: Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras 33D52: Basic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc.)
Type
Research Article
Information
Compositio Mathematica , Volume 151 , Issue 7 , July 2015 , pp. 1265 - 1287
Copyright
© The Authors 2015 

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