Quaternionic discrete series for Sp(1,1)

2007/03/27 by Seppanen, Henrik
#Differential Geometry (math.DG) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.math/0703797

Abstract

In this paper we study the analytic realisation of the discrete series representations for the group G=Sp(1,1) as a subspace of the space of square integrable sections in a homogeneous vector bundle over the symmetric space G/K:=Sp(1,1) /(Sp(1) × Sp(1)). We use the Szegö map to give expressions for the restrictions of the K-types occurring in the representation spaces to the submanifold AK/K.

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