Automorphic Representation of Unitary Groups in Three by Jonathan David Rogawski

By Jonathan David Rogawski

The function of this booklet is to boost the reliable hint formulation for unitary teams in 3 variables. The solid hint formulation is then utilized to procure a type of automorphic representations. This paintings represents the 1st case during which the solid hint formulation has been labored out past the case of SL (2) and comparable teams. Many phenomena on the way to look within the basic case current themselves already for those unitary groups.

Show description

Read or Download Automorphic Representation of Unitary Groups in Three Variables PDF

Best group theory books


This booklet is a accomplished advent to the speculation of solid commutator size, a tremendous subfield of quantitative topology, with significant connections to 2-manifolds, dynamics, geometric crew thought, bounded cohomology, symplectic topology, and lots of different topics. We use positive tools each time attainable, and concentrate on basic and specific examples.

Geometry and Cohomology in Group Theory

This quantity displays the fruitful connections among staff conception and topology. It comprises articles on cohomology, illustration idea, geometric and combinatorial crew thought. the various world's top recognized figures during this very energetic region of arithmetic have made contributions, together with giant articles from Ol'shanskii, Mikhajlovskii, Carlson, Benson, Linnell, Wilson and Grigorchuk that would be useful reference works for a few future years.

Rings, modules, and algebras in stable homotopy theory

This publication introduces a brand new point-set point method of strong homotopy thought that has already had many functions and grants to have an enduring impression at the topic. Given the sector spectrum $S$, the authors build an associative, commutative, and unital wreck product in an entire and cocomplete classification of ""$S$-modules"" whose derived type is corresponding to the classical good homotopy class.

Extra resources for Automorphic Representation of Unitary Groups in Three Variables

Example text

Let I be a regular element in T. 1, there exists 1' E H which is stably conjugate but not conjugate to I in G. (T, G) = Z/2. 8. Singular semisimple elements. Let G = U(3). For ~ E F*, let He be the unitary group in two variables defined by the Hermitian form: He The isomorphism class of depends only on ~ modulo NE* and we obtain a bijection between F* /NE* and the set of isomorphism classes of unitary groups in two variables over F with respect to E. The group H 1 is quasisplit and is isomorphic to U(2).

Let IP(T) be the set of unramified characters of T. (T, G)-orbit and every element of E"( G) is of the form 7r x for some x E Il"(T). Fix an element Wp E Wp whose projection to r(Fun /F) is the Frobenius element. (T, G) (and hence E"(G)) and the set of semisimple G- conjugacy classes in LG of the form {g x wp }. The conjugacy class {g(7r)} in LG associated to a representation 7r E E" ( G) is called the Langlands class of 7r. We can choose a representative g x wp with g E f. Let (H, s, T/) be an endoscopic datum for G.

Regular class in G. Suppose that 1' E TH. Then 1' is called ( G, H)-regular if a('ef;(I')) f. 1 for each root a of T which is not the image of a root of TH in H. Let 1' be a ( G, H)-regular element of TH. Suppose that 'lj; is defined over F (this entails no loss of generality since the choice of Tis arbitrary) and let I= 'ef;(1'). H in H -Y, and that of T in G-y. It follows that 'lj; extends to an isomorphism of H-y' with G-Y which is an inner twisting over F. In particular, we can identify Z(H-y') with Z(G-y) and, if Fis local, we can choose compatible measures on H-y' and G-y.

Download PDF sample

Rated 4.40 of 5 – based on 30 votes