Birgit Speh

Irreducible unitary representations of SU(2, 2)

We give an explicit classification of the irreducible unitary representations of the simple Lie group SU(2, 2).

Branching Laws for Some Unitary Representations of SL(4,R)

In this paper we consider the restriction of a unitary irreducible representation of type Aq( ) of GL(4,R) to reductive subgroups H which are the fixpoint sets of an involution. We obtain a formula for the restriction to the symplectic group and to GL(2,C), and as an application we construct in the last section some representations in the cuspidal spectrum of the symplectic and the complex general linear group. In addition to working directly with the cohmologically induced module to obtain the branching law, we also introduce the useful concept of pseudo dual pairs of subgroups in a reductive Lie group.

A Plancherel formula for L2(G∕H) for almost symmetric subgroups

In this paper we study the Plancherel formula for a new class of homogeneous spaces for real reductive Lie groups; these spaces are fibered over non-Riemannian symmetric spaces, and they exhibit a phenomenon of uniform infinite multiplicities. They also provide examples of non-tempered representations of the group appearing in the Plancherel formula. Several classes of examples are given.

Analytic torsion and automorphic forms

In this note we prove a vanishing theorem for the analytic torsion of a locally symmetric space.

Lefschetz Numbers and Cyclic Base Change for Purely Imaginary Extensions

Let S be a locally symmetric space and V locally constant sheaf on S such that an automorphism σ of finite order of the underlying real Lie group G ∞ acts on S and V.Then a Lefschetz number L(σ, S, V) of the induced σ-action on the cohomology H (S, V) is defined.

Derived Functors and Intertwining Operators for Principal Series Representations of \(SL_2({\pmb {\mathbb {R}}})\)

We consider the principal series representations \(I_\nu \) induced from a character \(\nu \) of the upper triangular matrices B and its realization on the Frechet space of \(C^\infty \)-sections of a line bundle over G / B. Its continuous dual is denoted by \(I_\nu ^*\). Let \(N \subset B\) be the nilpotent subgroup whose diagonal entries are 1 and denote by \({\mathfrak n }\) its Lie algebra. We determine \(H^0({\mathfrak n }, I_\nu ^*) \) and \(H^1({\mathfrak n },I_\nu ^*)\) and conclude that space of the intertwining operators \(T:I_\nu \rightarrow I_{-\nu }\) is 2 dimensional for some integral parameter, otherwise it is one dimensional. The intertwining operators are identified with distributions. We show that for certain parameters the support of this distribution is a point, i.e. that the intertwining operator is a differential intertwining operator.

A Comparison of Geometric Theta Functions for Forms of Orthogonal Groups

Let F be a totally real extension of ℚ, denote by V a finite dimensional F-vector space and by q a nondegenerate anisotropic form on V over F. We assume that G = ResF∣ℚ Spin(g) has an ℝ-fundamental torus of split rank 1 and fix a congruence subgroup Γ of G(ℚ).