Pfaffians and Shuffling Relations for the Spin Module

2012/03/13 by Rocco Chirivì, Chirivì, Rocco, Andrea Maffei +1 · 1 citation
Computer Science · Mathematics · #14M15 #20G05 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Matrix Theory and Algorithms #Representation Theory (math.RT) #math.RT #msc:14M15 #msc:20G05

paper · pdf · doi:10.48550/arxiv.1203.2943

10 pages

arxiv created 2012/03/13 · openalex publication_date 2012/03/13 · arxiv updated 2012/03/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present explicit formulas for a set of generators of the ideal of relations among the pfaffians of the principal minors of the antisymmetric matrices of fixed dimension. These formulas have an interpretation in terms of the standard monomial theory for the spin module of orthogonal groups.

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