Higher level BGG reciprocity for current algebras
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.
Cite
@article{arxiv.2207.07447,
title = {Higher level BGG reciprocity for current algebras},
author = {Syu Kato},
journal= {arXiv preprint arXiv:2207.07447},
year = {2025}
}
Comments
66pp, v4: Substantially revised. Streamlined exposition and added explanations at many places. Added Section 11 on (not affine) highest weight structures, and Appendix A on higher level $q$-Cauchy kernel identities