Real double flag varieties for the symplectic group

Abstract

In this paper we study a key example of a Hermitian symmetric space and a natural associated double flag variety, namely for the real symplectic group $G$ and the symmetric subgroup $L$, the Levi part of the Siegel parabolic $P_S$. We give a detailed treatment of the case of the maximal parabolic subgroups $Q$ of $L$ corresponding to Grassmannians and the product variety of $G/P_S$ and $L/Q$; in particular we classify the $L$-orbits here, and find natural explicit integral transforms between degenerate principal series of $L$ and $G$.

29 pages

References in corpus (2)

• Classification of finite-multiplicity symmetric pairs
• Double flag varieties for a symmetric pair and finiteness of orbits

Cited by in corpus (1)

• Enhanced zeta distributions and its functional equations