Izvorni znanstveni članak

https://doi.org/10.3336/gm.46.1.12

Rank one reducibility for unitary groups

Marcela Hanzer ; Department of Mathematics, University of Zagreb, 10000 Zagreb, Croatia

Sažetak

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.

Ključne riječi

Unitary groups over non-archimedean fields; reducibility of parabolic induction; theta correspondence

Hrčak ID:

68889

URI

https://hrcak.srce.hr/68889

Datum izdavanja:

13.6.2011.

Posjeta: 1.134 *