The distinction problems for Sp4 and SO3,3

Author:

Lu Hengfei1ORCID

Affiliation:

1. Department of Mathematics , Weizmann Institute of Science , 234 Herzl St. P.O.B. 26 , Rehovot 7610001 , Israel ; and Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, Wien 1090, Austria

Abstract

Abstract This paper studies the Prasad conjecture for the special orthogonal group SO 3 , 3 \mathrm{SO}_{3,3} . Then we use the local theta correspondence between Sp 4 \mathrm{Sp}_{4} and O ( V ) \mathrm{O}(V) to study the Sp 4 \mathrm{Sp}_{4} -distinction problems over a quadratic field extension E / F E/F and dim V = 4 \dim V=4 or 6. Thus we can verify the Prasad conjecture for a square-integrable representation of Sp 4 ( E ) \mathrm{Sp}_{4}(E) .

Funder

European Research Council

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,General Mathematics

Reference30 articles.

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