An example of non-homeomorphic conjugate varieties

We give examples of smooth quasi-projective varieties over complex numbers, in the context of connected Shimura varieties, which are not homeomorphic to a conjugate of itself by an automorphism of the complex numbers.Comment: 4 page

Unique decomposition of tensor products of irreducible representations of simple algebraic groups

We show that a tensor product of irreducible, finite dimensional representations of a simple Lie algebra over a field of characteristic zero, determines the individual constituents uniquely. This is analogous to the uniqueness of prime factorisation of natural numbers.Comment: 23 pages, to appear in Annals of Mathematic

On strong multiplicity one for automorphic representations

We extend the strong multiplicity one theorem of Jacquet, Piatetski-Shapiro and Shalika. Let $\pi$ be a unitary, cuspidal, automorphic representation of GL_n(\A_K). Let $S$ be a set of finite places of $K$, such that the sum $\sum_{v\in S}Nv^{-2/(n^2+1)}$ is convergent. Then $\pi$ is uniquely determined by the collection of the local components $\{\pi_v\mid v\not\in S, ~v \~\text{finite}\}$ of $\pi$. Combining this theorem with base change, it is possible to consider sets $S$ of positive density, having appropriate splitting behavior with respect to solvable extensions of $K$, and where $\pi$ is determined upto twisting by a character of the Galois group of $L$ over $K$.Comment: 8 page

On the vanishing of the measurable Schur cohomology groups of Weil groups

We generalize a theorem of Tate and show that the second cohomology of the Weil group of a global or local field with coefficients in \C^* (or more generally, with coefficients in the complex points of a tori over \C) vanish, where the cohomology groups are defined using measurable cochains in the sense of Moore. We recover a theorem of Labesse proving that admissible homomorphisms of a Weil group to the Langlands dual of a reductive group can be lifted to an extension of the Langlands dual group by a tori.Comment: To appear in Compositio Mathematica. Minor editing, and a conjecture in the earlier version on the vanishing of the higher cohomology groups of Weil groups is fals

Recovering modular forms and representations from tensor and symmetric powers

We consider the problem of determining the relationship between two representations knowing that some tensor or symmetric power of the original represetations coincide. Combined with refinements of strong multiplicity one, we show that if the characters of some tensor or symmetric powers of two absolutely irreducible $l$-adic representation with the algebraic envelope of the image being connected, agree at the Frobenius elements corresponding to a set of places of positive upper density, then the representations are twists of each other by a finite order character.Comment: 18 pages; this is a revised version of a paper submitted to the old Number Theory archive as ANT-035

A Consumer Logistics Framework for Understanding Preferences for High-Speed Rail Transportation, MTI Report 05-04

The prospect for high-speed rail (HSR) service for the San Francisco-Los Angeles corridor and beyond first arose eight years ago. The plan remains to connect California’s major cities in the next 15 years at a total cost of $25 billion. The purpose of this study is to reach a fuller understanding of consumers’ perceptions of such a service. Consumer logistics theory is used in the study as a framework to begin to provide this understanding of consumer perceptions and to inform future efforts to develop and market HSR service. This study uses the consumer logistics framework to help understand how various demographic groups, various groups defined by public transportation usage frequency, and various groups defined by HSR usage intention level perceive various logistical aspects of HSR service. The consumer logistics framework is also be used to develop a macro model that examines the relationship between performance of consumer logistics functions, perceptions of HSR travel value (consisting of travel efficiency and effectiveness), and HSR travel intention for intercity business commuters. The results show the manner and the extent to which the logistics of HSR are likely to lead to customer intentions to use it for inter-city transportation and how HSR service providers, by enhancing their consumer logistics capabilities, can encourage intended HSR usage between San Francisco and Los Angeles for business commuter