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Rank-level duality of conformal blocks for odd orthogonal Lie algebras in genus 0

Author: Swarnava Mukhopadhyay
Journal: Trans. Amer. Math. Soc. 368 (2016), 6741-6778
MSC (2010): Primary 17B67, 14H60; Secondary 32G34, 81T40
Published electronically: December 3, 2015
MathSciNet review: 3461050
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Abstract: Classical invariants for representations of one Lie group can often be related to invariants of some other Lie group. Physics suggests that the right objects to consider for these questions are certain refinements of classical invariants known as conformal blocks. Conformal blocks appear in algebraic geometry as spaces of global sections of line bundles on moduli stacks of parabolic bundles on a smooth curve. Rank-level duality connects a conformal block associated to one Lie algebra to a conformal block for a different Lie algebra. In this paper, we prove a rank-level duality for $ \mathfrak{so}(2r+1)$ conformal blocks on the pointed projective line which was suggested by T. Nakanishi and A. Tsuchiya.

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Additional Information

Swarnava Mukhopadhyay
Affiliation: Department of Mathematics, University of Maryland, College Park, Maryland 20742-4015

Keywords: Rank-level duality, infinite dimensional Lie algebras, moduli of curves, KZ-connection
Received by editor(s): August 9, 2013
Received by editor(s) in revised form: February 24, 2015
Published electronically: December 3, 2015
Additional Notes: The first author was supported in part by NSF grant #DMS-0901249.
Article copyright: © Copyright 2015 American Mathematical Society

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