ALGEBRAS OF INVARIANT FUNCTIONS ON THE SHILOV BOUNDARIES OF SIEGEL DOMAINS

Let D = G/K be a bounded symmetric domain and KIL the Shilov boundary of D. Let N be the Shilov boundary of the Siegel domain realization of G/K. We consider the case when D is the exceptional non-tube type dom ain of the type (e(6(-14)),so(10) x so(2)). We prove that (N x L, L) i s not a Gelfand pair and thus resolve an open question of G. Carcano.