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arXiv · 2409.06871

On Generalized Pfaffians

Jacques Distler·Nathan Donagi·Ron Donagi
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Abstract

The determinant of an anti-symmetric matrix $g$ is the square of its Pfaffian, which like the determinant is a polynomial in the entries of $g$. Studies of certain super conformal field theories (of class S) suggested a conjectural generalization of this, predicting that each of a series of other polynomials in the entries of $g$ also admit polynomial square roots. Among other consequences, this conjecture led to a characterization of the local Hitchin image for type D. Several important special cases had been established previously. In this paper we prove the conjecture in full.

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Jacques Distler, Nathan Donagi, Ron Donagi. 2024-09-10. On Generalized Pfaffians. https://arxiv.org/abs/2409.06871

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