Discrete series Whittaker functions on $Spin(2n,2)$

TL;DR

This paper investigates discrete series Whittaker functions on the group $Spin(2n, 2)$, explicitly determining the dimensions of their models and deriving integral formulas, advancing understanding of their structure and representations.

Contribution

It provides explicit dimension formulas for Whittaker models and Mellin-Barnes integral representations, linking them to representations of lower-rank groups.

Findings

Dimensions of algebraic and continuous Whittaker models are explicitly calculated.

Whittaker functions are expressed as sums involving irreducible representations of $Spin(2n-3, 2)$.

Integral formulas of Mellin-Barnes type are derived for these Whittaker functions.

Abstract

Discrete series Whittaker functions on $Spin(2n, 2)$ are studied. The dimensions of the space of both algebraic and continuous Whittaker models are explicitly determined. They are described by a sum of dimensions of irreducible representations of $Spin(2n-3, 2)$. Also obtained are the Mellin-Barnes type integral formulas of the Whittaker functions associated with minimal $K$-type vectors.