Glasnik Matematicki, Vol. 46, No.1 (2011), 121-148.

RANK ONE REDUCIBILITY FOR UNITARY GROUPS

Marcela Hanzer

Abstract.   Let (G,G') denote a dual reductive pair consisting of two unitary groups over a nonarchimedean local field of characteristic zero. We relate the reducibility of the parabolically induced representations of these two groups if the inducing data is cuspidal and related to each other by theta correspondence. We calculate theta lifts of the irreducible subquotients of these parabolically induced representations. To obtain these results, we explicitly calculate filtration of Jacquet modules of the appropriate Weil representation (as Kudla did for the orthogonal-symplectic dual pairs), but keeping in mind the explicit splittings of covers of these two unitary groups, also obtained by Kudla.

2000 Mathematics Subject Classification.   22E35, 22E50, 11F70.

Key words and phrases.   Unitary groups over non-archimedean fields, reducibility of parabolic induction, theta correspondence.

DOI: 10.3336/gm.46.1.12

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