On the local theta correspondence and R-groups
نویسندگان
چکیده
منابع مشابه
Local Theta Correspondence for Small Unitary Groups
In this paper we give an explicit parameterization of the local theta correspondence of supercuspidal representations for the reductive dual pairs (U1(F ),U1(F )), (U1(F ),U1,1(F )), (U1(F ),U2(F )), and (U1(F ),U1,2(F )) of unitary groups over a nonarchimedean local field F of odd residue characteristic.
متن کاملThe Theta Correspondence over R
These notes were written for the workshop on the Theta correspondence held at the University of Maryland, May 1994. They have circulated informally for many years. Except for minor changes and some improvements to the references they have not been changed. There have been too many developments in the field since 1994 to try to bring them up to date. This is dedicated to Roger Howe, who introduc...
متن کاملTheta Correspondence for Unitary Groups
In this paper we study the theta correspondence for Unitary groups of the same size over local and global fields. This correspondence has been studied in many cases by several authors. We are able to unify and generalise all these known results in terms of two conjectures, one local and the other global. These conjectures are in terms of the parametrisation of irreducible admissible representat...
متن کاملDegenerate Principal Series and Local Theta Correspondence
In this paper we determine the structure of the natural Ũ(n, n) module Ωp,q(l) which is the Howe quotient corresponding to the determinant character det of U(p, q). We first give a description of the tempered distributions on Mp+q,n(C) which transform according to the character det−l under the linear action of U(p, q). We then show that after tensoring with a character, Ωp,q(l) can be embedded ...
متن کاملDegenerate Principal Series and Local Theta Correspondence Iii: the Case of Complex Groups
Let (G, G) be one of the following complex dual pairs: (O(m,C), Sp(2n,C)), (GL(m,C),GL(2n,C)), (Sp(2m,C),O(4n,C)). We determine the relationship between the space ofG-coinvariants and certain degenerate principal series representations of G. We also show that the space of G-invariant distributions is generated by the Dirac distribution as a G-representation. Introduction and main results Let G ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Compositio Mathematica
سال: 2004
ISSN: 0010-437X,1570-5846
DOI: 10.1112/s0010437x03000228