A Howe-type correspondence for the dual pair (sl(2),sl(n)) in sl(2n)

TL;DR

This paper establishes a Howe correspondence for a specific family of representations of sl(2n), expanding the understanding of dual pairs in Lie algebra representation theory.

Contribution

It proves a Howe correspondence for a previously studied family of representations of sl(2n), providing new insights into dual pairs in Lie algebra theory.

Findings

Established a Howe correspondence for the family of representations of sl(2n)

Extended the understanding of dual pairs in Lie algebra representations

Connected to prior work by Benkart, Britten, and Lemire

Abstract

In this article we prove a Howe correspondence for a family of representations of sl(2n), which was introduced by Benkart, Britten, and Lemire.