TY - JOUR
T1 - Real double flag varieties for the symplectic group
AU - Nishiyama, Kyo
AU - Ørsted, Bent
PY - 2018/1/15
Y1 - 2018/1/15
N2 - 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 PS. 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/PS 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.
AB - 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 PS. 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/PS 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.
KW - Degenerate principal series representation
KW - Double flag variety
KW - Hermitian symmetric space
KW - Prehomogeneous vector space
UR - http://www.scopus.com/inward/record.url?scp=85025431155&partnerID=8YFLogxK
U2 - 10.1016/j.jfa.2017.07.003
DO - 10.1016/j.jfa.2017.07.003
M3 - Journal article
AN - SCOPUS:85025431155
SN - 0022-1236
VL - 274
SP - 573
EP - 604
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
IS - 2
ER -