Commutation relations of Hecke operators for Arakawa lifting

摘要

T. Arakawa. in his Unpublished note, constructed and Studied it theta lifting front elliptic cusp forms to automorphic forms on the quaternion unitary group Of Signature (1. q), The second named author proved that such a lifting provides bounded (or cuspidal) automorphic forms generating quaternionic discrete series. In this paper. restricting ourselves to the case of q = 1. we reformulate Arakawa's theta lifting as it theta correspondence in the adelic setting and determine a commutation relation of Hecke operators satisfied by the lifting. As in application, we show that the theta lift of an elliptic Hecke eigenform is also it Hecke eigenform On the quaternion unitary group. We furthermore Study the spinor L-function attached to the theta lift.