Pfaffians and Shuffling Relations for the Spin Module
Rocco Chiriv\`i, Andrea Maffei
TL;DR
This paper provides explicit formulas for relations among pfaffians of principal minors of antisymmetric matrices, linking them to the standard monomial theory for the spin module of orthogonal groups.
Contribution
It introduces new explicit formulas for the ideal of relations among pfaffians, connecting algebraic relations to representation theory of orthogonal groups.
Findings
Explicit formulas for generators of the relation ideal.
Interpretation in terms of standard monomial theory.
Connections to the structure of the spin module.
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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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Matrix Theory and Algorithms