28 research outputs found
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
Local newforms for the general linear groups over a non-archimedean local field
In [12], Jacquet--Piatetskii-Shapiro--Shalika defined a family of compact
open subgroups of -adic general linear groups indexed by non-negative
integers, and established the theory of local newforms for irreducible generic
representations. In this paper, we extend their results to all irreducible
representations. To do this, we define a new family of compact open subgroups
indexed by certain tuples of non-negative integers. For the proof, we introduce
the Rankin--Selberg integrals for Speh representations.Comment: 60 page