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arXiv · 2608.24548

A new antisymmetrizer-to-determinant formula and a conjecture of Colomo and Pronko

Ilse Fischer·Markus Reibnegger
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Abstract

Identities asserting that an antisymmetrizer admits a determinantal expression are central to several proofs of counting formulas for alternating sign matrices. Antisymmetrizers appear also frequently in symmetric function theory as, for instance, the Hall-Littlewood polynomials can be realized via antisymmetrizers. In this paper, we establish a new identity of this type, thereby proving a conjecture of Lukas Riegler and one of the authors. We also elaborate on a related antisymmetrizer that may be pivotal in resolving a beautiful conjecture of Colomo and Pronko, and we formulate a version of their conjecture tailored to the suggested approach.

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Ilse Fischer, Markus Reibnegger. 2026-08-25. A new antisymmetrizer-to-determinant formula and a conjecture of Colomo and Pronko. https://arxiv.org/abs/2608.24548

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