Special Reduced Multiplets and Minimal Representations for Sp(n,R)

TL;DR

This paper advances the systematic construction of invariant differential operators for Sp(n,R) by introducing special reduced multiplets and minimal representations, expanding the understanding of these mathematical structures.

Contribution

It provides the first detailed description of special reduced multiplets and minimal representations for Sp(n,R), building on previous work on main multiplets.

Findings

Defined special reduced multiplets for Sp(n,R)

Constructed minimal representations for Sp(n,R)

Extended the classification of invariant differential operators

Abstract

In the present paper we continue the programme of systematic construction of invariant differential operators on the example of the non-compact groups Sp(n,R). Earlier in arXiv:1205.5521 we gave the main multiplets and the main reduced multiplets of indecomposable elementary representations including the necessary data for all relevant invariant differential operators. Here we give the special reduced multiplets and the minimal representations of Sp(n,R).