Real Shintani Functions and Multiplicity Free Property for the Symmetric Pair $\bigl(SU(2,1), S(U(1,1) × U(1))\bigr)$

J. Math. Sci. Univ. Tokyo
Vol. 4 (1997), No. 3, Page 663--727.

Tsuzuki, Masao
Real Shintani Functions and Multiplicity Free Property for the Symmetric Pair $\bigl(SU(2,1), S(U(1,1) × U(1))\bigr)$
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Abstract:
We shall present an explicit formula of "generalized" spherical functions on $SU(2,1)$ with respect to its reductive spherical subgroup $S\bigl(U(1,1) × U(1)\bigr)$, which can be considered to be a real analogue of the Whittaker-Shintani functions introduced by Shintani and investigated by Murase and Sugano. At the same time, we shall prove a multiplicity one theorem for the corresponding space of intertwining operators.

Mathematics Subject Classification (1991): Primary 11F70; Secondary 22E46, 33C05, 11F67
Mathematical Reviews Number: MR1484607

Received: 1997-02-25