Rad HAZU, Matematičke znanosti, Vol. 19 (2015), 55-68.

GENERALIZED SHALIKA MODEL ON SO4n(F), SYMPLECTIC LINEAR MODEL ON Sp4n(F) AND THETA CORRESPONDENCE

Marcela Hanzer

Department of Mathematics, University of Zagreb, 10 000 Zagreb, Croatia
e-mail: hanmar@math.hr

Abstract.   We show that if an irreducible admissible representation of SO4n(F) has a generalized Shalika model, then its small theta lift to Sp4n(F) has the symplectic linear model, thus answering a question posed by D. Jiang. Here F is a non-archimedean field of characteristic zero.

2010 Mathematics Subject Classification.   22E50, 11F70.

Key words and phrases.   Generalized Shalika model, symplectic linear model, theta correspondence.

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