On the Plancherel measure for linear Lie groups of rank one

In this paper we find a very explicit, simple form for the Plancherel measure for rank one, linear simple groups, including the normalizing constant.     

The spectrum of twisted Dirac operators on compact flat manifolds

Let be an orientable compact flat Riemannian manifold endowed with a spin structure. In this paper we determine the spectrum of Dirac operators acting on smooth sections of twisted spinor bundles of , and we derive a formula for the corresponding eta series. In the case of manifolds with holonomy group , we give a very simple expression for the multiplicities of eigenvalues that allows us to compute explicitly the -series, in terms of values of Hurwitz zeta functions, and the -invariant. We give the dimension of the space of harmonic spinors and characterize all -manifolds having asymmetric Dirac spectrum.

Furthermore, we exhibit many examples of Dirac isospectral pairs of -manifolds which do not satisfy other types of isospectrality. In one of the main examples, we construct a large family of Dirac isospectral compact flat -manifolds, pairwise nonhomeomorphic to each other of the order of .

     

Bounded isometries and homogeneous Riemannian quotient manifolds

Let M be a Riemannian manifold that admits a transitive semisimple group G of isometries, G of noncompact type. Then every bounded isometry of M centralizes G and so is a Clifford translation (constant displacement). Thus a Riemannian quotient M is homogeneous if and only if consists of Clifford translations of M. The technique of proof also leads to a determination of the group of all isometries of M.IMAF, Córdoba, Argentina. Partially supported by Conicet, Argentina, and by IMPA, Rio de Janeiro, Brazil.IMAF, Córdoba, Argentina. Partially supported by Conicet, Argentina.University of California at Berkely, U.S.A. Partially supported by National Science Foundation Grant DMS-8200235.     

FTIR Emission Spectra, Molecular Constants, and Potential Curve of Ground State GeO

Extensive new high-temperature, high-resolution FTIR emission spectroscopy measurements for the five common isotopomers of GeO are combined with previous diode laser and microwave measurements in combined isotopomer analyses. New Dunham expansion parameters and an accurate analytical potential energy function are determined for the ground X1Sigma+ state. Copyright 1999 Academic Press.     

$${\mathbb{Z}}_2^k$$ -Manifolds are isospectral on forms

We obtain a simple formula for the multiplicity of eigenvalues of the Hodge-Laplace operator, Δ _f , acting on sections of the full exterior bundle over an arbitrary compact flat Riemannian n-manifold M with holonomy group , 1 ≤ k ≤ n − 1. This formula implies that any two such manifolds having isospectral lattices of translations are isospectral with respect to Δ _f . As a consequence, we construct a large family of pairwise Δ _f -isospectral and nonhomeomorphic n-manifolds of cardinality greater than . Supported by Conicet, Secyt-UNC.