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Let D = G/K be a bounded symmetric domain and K/L 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 domain of the type (e6(−14), so(10)× so(2)). We prove that (N o L, L) is not a Gelfand pair and thus resolve an open question of G. Carcano.

Algebras of invariant functions on the Shilov boundaries of Siegel domains