On the tensor product of theta representations of GL₃

Gordan Savin

Vol. 154 (1992), No. 2, 369–380

DOI: 10.2140/pjm.1992.154.369

Abstract

Let V be the theta representation of GL₃—the two fold central extension of GL₃. Let W be a spherical representation of GL₃. We show that there is a nonzero GL₃ invariant trilinear form on V ⊗V ^∗⊗W if and only if W is a lift from SL₂. In this case the form is unique up to a scalar.

Mathematical Subject Classification 2000

Primary: 11F70

Secondary: 11F27, 11F85, 22E35, 22E50

Milestones

Received: 12 March 1991

Published: 1 June 1992