Orthosymplectic Cauchy identities

TL;DR

This paper provides bijective proofs of orthosymplectic Cauchy identities using new insertion algorithms, extending classical identities to the orthosymplectic setting.

Contribution

It introduces two orthosymplectic insertion algorithms that generalize Berele's symplectic insertion, enabling bijective proofs of orthosymplectic Cauchy identities.

Findings

Established bijective proofs for orthosymplectic Cauchy identities.

Developed orthosymplectic insertion algorithms based on Berele's methods.

Extended classical symplectic identities to the orthosymplectic case.

Abstract

We give bijective proofs of orthosymplectic analogues of the Cauchy identity and dual Cauchy identity for orthosymplectic Schur functions. To do so, we present two insertion algorithms; these are orthosymplectic versions of Berele's symplectic insertion algorithms, which were used by Sundaram to give bijective proofs of Cauchy identities for symplectic Schur functions.