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Strange duality of Verlinde spaces for \(G_2\) and \(F_4\)

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Abstract

We prove that the pull back of the canonical theta divisor for \(E_8\)-bundles at level one induces a strange duality between Verlinde spaces for \(G_2\) and \(F_4\) at level one on smooth curves of genus g. We also prove a parabolic generalization in terms of conformal blocks and write down identities between conformal blocks divisors in \({\text {Pic}}(\overline{{\text {M}}}_{g,n})_{{\mathbb {Q}}}\).

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Acknowledgments

I thank Jeffrey Adams, Shrawan Kumar and Richard Wentworth for useful conversations during the preparation of this paper. This work was initiated by a question (see Theorem 1.1) conveyed to the author by Christian Pauly. I thank him for his comments and suggestions. I was supported by Simons Travel grant.

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Correspondence to Swarnava Mukhopadhyay.

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Mukhopadhyay, S. Strange duality of Verlinde spaces for \(G_2\) and \(F_4\) . Math. Z. 283, 387–399 (2016). https://doi.org/10.1007/s00209-015-1603-8

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