Local duality of Hecke operators for symplectic and orthogonal groups

A formula for the duality of Hecke operators for symplectic and orthogonal groups on spaces of local Weil representations is obtained in terms of spherical functions.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademii Nauk SSSR, Vol. 185, pp. 37–59, 1990.