An orthosymplectic Pieri rule

TL;DR

This paper introduces a Pieri rule for orthosymplectic characters, linking it to Sundaram's rule for symplectic characters and showing they follow the same multiplication rules.

Contribution

It establishes a Pieri rule for orthosymplectic characters and connects it to existing symplectic character rules, expanding combinatorial understanding.

Findings

Orthosymplectic Pieri rule matches Sundaram's rule for symplectic characters

Orthosymplectic and symplectic characters obey the same product rule

Provides a combinatorial rule for orthosymplectic character multiplication

Abstract

The classical Pieri formula gives a combinatorial rule for decomposing the product of a Schur function and a complete homogeneous symmetric polynomial as a linear combination of Schur functions with integer coefficients. We give a Pieri rule for describing the product of an orthosymplectic character and an orthosymplectic character arising from a one-row partition. We establish that the orthosymplectic Pieri rule coincides with Sundaram's Pieri rule for symplectic characters and that orthosymplectic characters and symplectic characters obey the same product rule.