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

Mukhopadhyay, Swarnava

doi:10.1090/tran6691

Rank-level duality of conformal blocks for odd orthogonal Lie algebras in genus $0$
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Trans. Amer. Math. Soc. 368 (2016), 6741-6778 Request permission

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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