Parahoric induction and chamber homology for SL2

We consider the special linear group G=SL2 over a p-adic field, and its diagonal subgroup M=GL1. Parabolic induction of representations from M to G induces a map in equivariant homology, from the Bruhat-Tits building of M to that of G. We compute this map at the level of chain complexes, and show that it is given by parahoric induction (as defined by J.-F. Dat).Comment: 19 page

Freshwater Biology

Since the declaration of the Moor House National Nature Reserve, a certain amount of work on freshwater biology and related subjects has been done within the boundaries of the reserve. This is a review of work undertaken between 1952 and 1973. Moor House Occasional Paper No. 5 (1973) reviewed published information on freshwaters and their fauna within the Moor House National Nature Reserve and surrounding area. This second edition up-dates the part of the account which dealt with the freshwaters and their invertebrate fauna by correcting errors and omissions from the original account and by adding information published sinoe 1973. The original account included brief sections on aquatic flora and on fish. These subjects are omitted from the 2nd editionbecause they will be covered by separate contributions to the series of OCcasional Paper

Material Sight: A Sensorium for Fundamental Physics

Often our attempts to connect to the spatial and temporal scales of fundamental physics - from the subatomic to the multiverse - provoke a form of perceptual vertigo, especially for non-scientists. When we approach ideas of paralysing abstraction through the perceptual range of our sensing bodies, a ‘phenomenological dissonance’ can be said to be invoked, between material presence and radical remoteness. This relational dynamic, between materiality and remoteness, formed the conceptual springboard for 'Material Sight' (2016-2018), a research project based at three world-leading facilities for fundamental physics, that brought to fruition a body of photographic objects, film works and immersive soundscape that re-presented the spaces of fundamental physics as sites of material encounter. The research was premised on a paradoxical desire to create a sensorium for fundamental physics, asking if photography, film and sound can embody the spaces of experimental science and present them back to scientists and non-scientists alike, not as illustrations of the technical sublime but as sites of phenomenological encounter. This article plots the key conceptual coordinates of 'Material Sight' and looks at how the project’s methodological design – essentially the production of knowledge through the 'act of looking' – emphatically resisted the gravitational pull of art to be instrumentalised as an illustrative device within scientific contexts

Effects of flow regime on the young stages of salmonid fishes. Summary and conclusions based on results for 1981-1985

The main British salmonid species spawn in clean gravel in streams and rivers, many of them in the upland areas of Britain. The earliest stages of the life cycle (eggs and alevins) spend some months within the gravel of the river bed. During this period their survival rate can be strongly influenced by flow regime and by related phenomena such as movement of coarse river bed material, changes in water level and the deposition of silt. In recent years human influence upon the flow regimes of upland water courses and upon the sediment inputs to them has increased. In order to conserve and, if possible, enhance the populations of salmonid fishes a deeper understanding of the interrelationships between survival of young salmonids and flow-related phenomena is needed. The acquisition of appropriate information is the main aim of the present project, which included: Studies on silt movement and the infilling of gravel voids by fine sediments, together with initial studies on the relationship between intragravel oxygen supply rate and the survival of intragravel stages of salmonids; studies in the general field of egg washout. The latter investigated the physical background to gravel bed disruption, the examination of the physical characteristics of sites chosen for redds, dimensions of redds and burial depth of eggs relative to the size of the fish constructing the redd and a series of smaller studies on other aspects of egg washout

Descent of Hilbert C*-modules

Let F be a right Hilbert C*-module over a C*-algebra B, and suppose that F is equipped with a left action, by compact operators, of a second C*-algebra A. Tensor product with F gives a functor from Hilbert C*-modules over A to Hilbert C*-modules over B. We prove that under certain conditions (which are always satisfied if, for instance, A is nuclear), the image of this functor can be described in terms of coactions of a certain coalgebra canonically associated to F. We then discuss several examples that fit into this framework: parabolic induction of tempered group representations; Hermitian connections on Hilbert C*-modules; Fourier (co)algebras of compact groups; and the maximal C*-dilation of operator modules over non-self-adjoint operator algebras.Comment: 37 pages. Fixed a typo in the definition of curvature in Definition 6.

Frobenius reciprocity and the Haagerup tensor product

In the context of operator-space modules over C*-algebras, we give a complete characterisation of those C*-correspondences whose associated Haagerup tensor product functors admit left adjoints. The characterisation, which builds on previous joint work with N. Higson, exhibits a close connection between the notions of adjoint operators and adjoint functors. As an application, we prove a Frobenius reciprocity theorem for representations of locally compact groups on operator spaces: the functor of unitary induction for a closed subgroup H of a locally compact group G admits a left adjoint in this setting if and only if H is cocompact in G. The adjoint functor is given by Haagerup tensor product with the operator-theoretic adjoint of Rieffel's induction bimodule.Comment: 18 pages. Final version, to appear in Trans. Amer. Math. So

Effects of flow regime on the young stages of Salmonid fishes. Conclusions based on results for 1977-1981

Rivers in Teesdale and its fish population have been monitored for several years. This report briefly describes the life cycle of British salmonid fishes and indicates the main ways in which this life cycle is influenced by discharge and related effects. Some highlights of the research results for 1977 - 1981 are briefly stated and proposals for future research are listed. Some practical implications of the results are discussed. (PDF contains 34 pages

Aspects of the washout of salmonid eggs. 5. Attempts to assess the importance of washout as a cause of mortailty

The paper reviews the methodology of attempts to assess the importance of washout as a cause of loss of salmonid eggs and alevins. The results of this study are presented of various small-scale field trials using buried artificial salmonid eggs and tethered table tennis balls. The results suggested that, even when few eggs were actually lost by washout, some downstream movement of the upper layers of gravel and of artificial eggs might have taken place

Fredholm modules over graph C*-algebras

We present two applications of explicit formulas, due to Cuntz and Krieger, for computations in K-homology of graph C*-algebras. We prove that every K-homology class for such an algebra is represented by a Fredholm module having finite-rank commutators; and we exhibit generating Fredholm modules for the K-homology of quantum lens spaces.Comment: 14 page