Macdonald Polynomials and BGG reciprocity for current algebras
Matthew Bennett, Arkady Berenstein, Vyjayanthi Chari, Anton Khoroshkin, and Sergey Loktev
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Abstract
We study the category of graded representations with finite--dimensional graded pieces for the current algebra associated to a simple Lie algebra. This category has many similarities with the category of modules for and in this paper, we use the combinatorics of Macdonald polynomials to prove an analogue of the famous BGG duality in the case of .
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Nonlinear Waves and Solitons