Higher level BGG reciprocity for current algebras

2022/07/15 by Kato, Syu · 1 citation
#FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2207.07447

Abstract

We exhibit a higher-level analogue of the Bernstein-Gelfand-Gelfand (BGG) reciprocity for twisted current algebras for each positive integer, which recovers the original one (established by Bennett, Berenstein, Chari, Ion, Khoroshkin, Loktev, and Manning) as its level-one case. This work brings theta functions and modular forms into the theory of symmetric polynomials. Furthermore, we establish branching properties for both versions of Demazure modules and provide a new interpretation of level-restricted generalized Kostka polynomials in terms of symmetric polynomials.

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