Pullbacks of hermitian Maass lifts

We consider pullbacks of hermitian Maass lifts of degree 2 to the diagonal matrices. By using the pullbacks, we give an explicit formura for central values of L-functions for GL(2)*GL(2).Comment: 59 pages, 0 figure

An analogue of ladder representations for classical groups

In this paper, we introduce a notion of ladder representations for split odd special orthogonal groups and symplectic groups over a non-archimedean local field of characteristic zero. This is a natural class in the admissible dual which contains both strongly positive discrete series representations and irreducible representations with irreducible A-parameters. We compute Jacquet modules and the Aubert duals of ladder representations, and we establish a formula to describing ladder representations in terms of linear combinations of standard modules.Comment: 24 page

The Zelevinsky-Aubert duality for classical groups (Automorphic forms, Automorphic representations, Galois representations, and its related topics)

In 1980, Zelevinsky [14] studied the representation theory of p-adic general linear groups. He introduced an involution on the Grothendieck group of smooth representations of finite length, which exchanges the trivial representation with the Steinberg representation. In fact, he conjectured that it preserves the irreducibility. Aubert [5] extended this involution to p-adic reductive groups, which is now called the Zelevinsky-Aubert duality. It is expected that this duality preserves the unitarity. In this article, based on the joint work with Alberto Mfnguez [3], we give an algorithm to compute the Zelevinsky-Aubert duality for odd special orthogonal groups or symplectic groups