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

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 $\bigl(SU(2,1), S(U(1,1) Ã U(1))\bigr)$
We shall present an explicit formula of "generalized" spherical functions on $SU(2,1)$ with respect to its reductive spherical subgroup $S\bigl(U(1,1) Ã U(1)\bigr)$, 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.