The $(g,K)$-module structures of principal series representations of $Sp(3,R)$

TL;DR

This paper explicitly describes the $(g,K)$-module structures of principal series representations of $Sp(3,R)$ and uses this to identify the associated holonomic systems for Whittaker functions.

Contribution

It provides a detailed explicit description of the $(g,K)$-modules for $Sp(3,R)$ principal series, advancing understanding of their structure and related Whittaker functions.

Findings

Explicit $(g,K)$-module structures for $Sp(3,R)$ principal series

Identification of holonomic systems for Whittaker functions

Enhanced understanding of representation theory of $Sp(3,R)$

Abstract

We describe explicitly the whole structures of the $(g,K)$-modules of principal series representations of $Sp(3,R)$. We apply this result to determine the holonomic system characterizing those Whittaker functions.