Principal series of Hermitian Lie groups induced from Heisenberg parabolic subgroups

Abstract: Let

G

be an irreducible Hermitian Lie group and

D = G / K

its bounded symmetric domain in

m a t h b b C^{d}

of rank

r

. Each

g a m m a

of the Harish-Chandra strongly orthogonal roots

g a m m a_{1}, c d o t s, g a m m a_{r}

defines a Heisenberg parabolic subgroup

P = M A N

of

G

. We study the principal series representations

I n d_{P}^{G} (1 o t i m e s e^{u} o t i m e s 1)

of

G

induced from

P

. We find the complementary series, reduction points, and unitary subrepresentations in this family of representations.

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