Casimir operators for symplectic groups

TL;DR

This paper constructs explicit Casimir operators for symplectic groups of any genus, providing a basis that clarifies their action on known representations, with illustrative examples.

Contribution

It introduces a complete set of Casimir operators for symplectic groups and a basis that simplifies understanding their action on representations.

Findings

Explicit formulas for Casimir operators for all symplectic groups

A basis that makes the action on known representations transparent

Examples illustrating the application of the operators

Abstract

We give a full set of Casimir operators for the symplectic group of arbitrary genus in terms of a basis chosen such that the action on representations of known $K$-type becomes transparent. We give examples for the latter.