Multiplicity one theorems: the Archimedean case

Let $G$ be one of the classical Lie groups \GL_{n+1}(\R), \GL_{n+1}(\C), \oU(p,q+1), \oO(p,q+1), \oO_{n+1}(\C), \SO(p,q+1), \SO_{n+1}(\C), and let $G'$ be respectively the subgroup \GL_{n}(\R), \GL_{n}(\C), \oU(p,q), \oO(p,q), \oO_n(\C), \SO(p,q), \SO_n(\C), embedded in $G$ in the standard way. We show that every irreducible Casselman-Wallach representation of $G'$ occurs with multiplicity at most one in every irreducible Casselman-Wallach representation of $G$. Similar results are proved for the Jacobi groups \GL_{n}(\R)\ltimes \oH_{2n+1}(\R), \GL_{n}(\C)\ltimes \oH_{2n+1}(\C), \oU(p,q)\ltimes \oH_{2p+2q+1}(\R), \Sp_{2n}(\R)\ltimes \oH_{2n+1}(\R), \Sp_{2n}(\C)\ltimes \oH_{2n+1}(\C), with their respective subgroups \GL_{n}(\R), \GL_{n}(\C), \oU(p,q), \Sp_{2n}(\R), \Sp_{2n}(\C).Comment: To appear in Annals of Mathematic

Design Criteria for Zero Leakage Connectors for Launch Vehicles. Mathematical Model of Interface Sealing Phenomenon, Volume 2 Final Report

Mathematical model of interface sealing phenomenon in determining design criteria for zero leakage connectors for launch vehicle

The sectional curvature remains positive when taking quotients by certain nonfree actions

We study some cases when the sectional curvature remains positive under the taking of quotients by certain nonfree isometric actions of Lie groups. We consider the actions of the groups $S^1$ and $S^3$ such that the quotient space can be endowed with a smooth structure using the fibrations $S^3/S^1{\simeq}S^2$ and $S^7/S^3\simeq S^4$. We prove that the quotient space carries a metric of positive sectional curvature, provided that the original metric has positive sectional curvature on all 2-planes orthogonal to the orbits of the action.Comment: 26 pages, 1 figure. Changed the spelling of the author's nam

Nonnegatively curved homogeneous metrics obtained by scaling fibers of submersions

We consider invariant Riemannian metrics on compact homogeneous spaces G/H where an intermediate subgroup K between G and H exists, so that the homogeneous space G/H is the total space of a Riemannian submersion. We study the question as to whether enlarging the fibers of the submersion by a constant scaling factor retains the nonnegative curvature in the case that the deformation starts at a normal homogeneous metric. We classify triples of groups (H,K,G) where nonnegative curvature is maintained for small deformations, using a criterion proved by Schwachh\"ofer and Tapp. We obtain a complete classification in case the subgroup H has full rank and an almost complete classification in the case of regular subgroups.Comment: 23 pages; minor revisions, to appear in Geometriae Dedicat

Four-qubit entanglement from string theory

We invoke the black hole/qubit correspondence to derive the classification of four-qubit entanglement. The U-duality orbits resulting from timelike reduction of string theory from D=4 to D=3 yield 31 entanglement families, which reduce to nine up to permutation of the four qubits.Comment: 4 pages, 1 figure, 2 tables, revtex; minor corrections, references adde

Recent Deformation in the Bottom Sediments of Western and Southeastern Lake Ontario and its Association with Major Structures and Seismicity

Geophysical surveys, undertaken in the Toronto-Burlington corridor of western Lake Ontario and in the Rochester Basin of southeastern Lake Ontario, revealed the presence of features affecting the young lake-bottom sediments. In the western part of the lake, they include inferred pop-ups in bedrock, and plumose structures, dark linear patterns, and linear belts of circular to elliptical signatures in the modern mud. In southeastern Lake Ontario the glacial and post-glacial sediments display vertical separations of on the order of 10-15 m. Pop-ups are tectonically-induced structures. The features in the modern mud commonly parallel the orientation of P-stresses measured in Paleozoic rocks nearby and, along with the pop-ups, are spatially related to an aeromagnetic lineament. Furthermore, all of these features occur within a seismically active belt. The vertical displacements of the layered glacial and post-glacial sediments, within the Rochester Basin, are located along the southern margin of the postulated WSW extension of the seismically active St. Lawrence rift system and are interpreted to be due to faulting. The geologically young age of the sediments affected by the various deformational features, along with the characteristics of the features themselves, suggest that the lake-bottom sediments surveyed in this study may have recorded the effects of neotectonic processes.Des levés géophysiques effectués dans le corridor Toronto-Burlington, dans l'ouest du lac Ontario, a révélé la présence d'éléments qui altèrent les jeunes sédiments lacustres du fond. Dans la partie ouest du lac, dans la roche en place, il s'agit de structures de soulèvement (pop-ups) et, dans les boues récentes, de structures plumeuses, de réseaux de traits sombres et de zones linéaires de tracés circulaires à elliptiques. Dans la partie sud-est du lac Ontario, il y a dans les sédiments glaciaires et postglaciaires des rejets verticaux de l'ordre de 10 à 15 m. Les structures de soulèvement sont d'origine tectonique. Les formes dans les boues récentes, généralement parallèles à l'orientation des contraintes de compression mesurées dans les roches paléozoïques voisines, sont spatialement reliés, comme les structures de soulèvement, à un linéament aéromagnétique. De plus, toutes ces formes se trouvent dans une zone sismique active. Les rejets verticaux dans les sédiments glaciaires et postglaciaires stratifiés, à l'intérieur du basssin de Rochester, sont localisés le long de la bordure sud du prolongement présumé WSW du système actif du rift du Saint-Laurent et sont probablement attribuables à la formation de failles. La jeunesse des sédiments altérés par les déformations et les caractéristiques des déformations mêmes laissent croire que ces sédiments ont probablement enregistré les effets de processus néotectoniques.Geophysikalische Vermessungen, die im Toronto Burlington-Korridor des westlichen Ontariosees und im Rochester-Becken des sùdôstlichen Ontariosees durchgefùhrt wurden, deckten die Anwesenheit von Elementen auf, welche auf die jungen Seegrundsedimente einwirken. Im westlichen Teil des Sees bestehen sie aus Hebungen im anste-henden Gestein und im modernen Schlamm aus federartigen Strukturen, dunklen linearen Mustern und linearen Gùrteln mit kreisformigen bis ellipsenfôrmigen Umrissen. Im sùdôstlichen Ontariosee gibt es in den glazialen und postglazialen Sedimenten verti-kale Verwùrfe der GrôRenordnung von 10-15 m. Die Hebungen sind tektonischen Ursprungs. Die Formen im modernen Schlamm liegen im allgemeinen paralell zu der Orientierung der in den benachbarten palàozoischen Felsen gemessenen P-Stresse und sind zusammen mit den Hebungen ràumlich mit einem aeromagnetischen Lineament verbunden. AuRerdem treten aile dièse Formen innerhalb eines seismisch aktiven Gùrtels auf. Die vertikalen Verstellungen der geschichteten glazialen und postglazialen Sedimente innerhalb des Rochester-Beckens werden entlang des sùdlichen Rands der angenommenen WSW-Verlàngerung des seismisch aktiven Sankt-Lorenz-Spaltensystems lokalisiert. Das geologisch relativ junge Alter der durch die verschiedenen Verformungen Iàf3t vermu-ten, daB die in dieser Studie gemessenen Seegrundsedimente moglicherweise die Wirkungen neotektonischer Prozesse aufgezeichnet haben

The resource theory of quantum reference frames: manipulations and monotones

Every restriction on quantum operations defines a resource theory, determining how quantum states that cannot be prepared under the restriction may be manipulated and used to circumvent the restriction. A superselection rule is a restriction that arises through the lack of a classical reference frame and the states that circumvent it (the resource) are quantum reference frames. We consider the resource theories that arise from three types of superselection rule, associated respectively with lacking: (i) a phase reference, (ii) a frame for chirality, and (iii) a frame for spatial orientation. Focussing on pure unipartite quantum states (and in some cases restricting our attention even further to subsets of these), we explore single-copy and asymptotic manipulations. In particular, we identify the necessary and sufficient conditions for a deterministic transformation between two resource states to be possible and, when these conditions are not met, the maximum probability with which the transformation can be achieved. We also determine when a particular transformation can be achieved reversibly in the limit of arbitrarily many copies and find the maximum rate of conversion. A comparison of the three resource theories demonstrates that the extent to which resources can be interconverted decreases as the strength of the restriction increases. Along the way, we introduce several measures of frameness and prove that these are monotonically nonincreasing under various classes of operations that are permitted by the superselection rule.Comment: 37 pages, 4 figures, Published Versio

Forms on Vector Bundles Over Hyperbolic Manifolds and the Conformal Anomaly

We study gauge theories based on abelian $p-$forms on real compact hyperbolic manifolds. An explicit formula for the conformal anomaly corresponding to skew--symmetric tensor fields is obtained, by using zeta--function regularization and the trace tensor kernel formula. Explicit exact and numerical values of the anomaly for $p-$forms of order up to $p=4$ in spaces of dimension up to $n=10$ are then calculated.Comment: 13 pages, 2 table

Statistical Mechanics of Membrane Protein Conformation: A Homopolymer Model

The conformation and the phase diagram of a membrane protein are investigated via grand canonical ensemble approach using a homopolymer model. We discuss the nature and pathway of $\alpha$-helix integration into the membrane that results depending upon membrane permeability and polymer adsorptivity. For a membrane with the permeability larger than a critical value, the integration becomes the second order transition that occurs at the same temperature as that of the adsorption transition. For a nonadsorbing membrane, the integration is of the first order due to the aggregation of $\alpha$-helices.Comment: RevTeX with 5 postscript figure