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arXiv · 2504.07184

Hermite Reciprocity and Self-Duality of Generalized Eagon-Northcott Complexes

Ethan Reed
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Abstract

Previous examples of self-duality for generalized Eagon-Northcott complexes were given by computing the divisor class group for Hankel determinantal rings. We prove a new case of self-duality of generalized Eagon-Northcott complexes with input being a map defining a Koszul module with nice properties. This choice of Koszul module can be specialized to the Weyman module, which was used in a proof of the generic version of Green's conjecture. In this case, the proof uses a version of Hermite Reciprocity not previously defined in the literature.

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Ethan Reed. 2025-04-09. Hermite Reciprocity and Self-Duality of Generalized Eagon-Northcott Complexes. https://arxiv.org/abs/2504.07184

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