Torsion in the cohomology of congruence subgroups of SL(4,Z) and Galois representations

We report on the computation of torsion in certain homology theories of congruence subgroups of SL(4,Z). Among these are the usual group cohomology, the Tate-Farrell cohomology, and the homology of the sharbly complex. All of these theories yield Hecke modules. We conjecture that the Hecke eigenclasses in these theories have attached Galois representations. The interpretation of our computations at the torsion primes 2,3,5 is explained. We provide evidence for our conjecture in the 15 cases of odd torsion that we found in levels up to 31

Mod 2 homology for GL(4) and Galois representations

We extend the computations in [AGM4] to find the mod 2 homology in degree 1 of a congruence subgroup Gamma of SL(4,Z) with coefficients in the sharbly complex, along with the action of the Hecke algebra. This homology group is closely related to the cohomology of Gamma with F_2 coefficients in the top cuspidal degree. These computations require a modification of the algorithm to compute the action of the Hecke operators, whose previous versions required division by 2. We verify experimentally that every mod 2 Hecke eigenclass found appears to have an attached Galois representation, giving evidence for a conjecture in [AGM4]. Our method of computation was justified in [AGM5]

Resolutions of the Steinberg module for GL(n)

We give several resolutions of the Steinberg representation St_n for the general linear group over a principal ideal domain, in particular over Z. We compare them, and use these results to prove that the computations in [AGM4] are definitive. In particular, in [AGM4] we use two complexes to compute certain cohomology groups of congruence subgroups of SL(4,Z). One complex is based on Voronoi's polyhedral decomposition of the symmetric space for SL(n,R), whereas the other is a larger complex that has an action of the Hecke operators. We prove that both complexes allow us to compute the relevant cohomology groups, and that the use of the Voronoi complex does not introduce any spurious Hecke eigenclasses

Agricultural resource priorities and recommendations for the Avon River Basin Natural Resource Management Strategy

This report for the Avon Natural Resource Management Strategy provides an assessment of the current status of land resources throughout the Avon River Basin in Western Australia. It identifies the sub-regions and landscape components of the area and the land resource assets. The greatest threats are salinity, soil acidification, subsurface compaction, waterlogging, water and wind erosion, and biosecurity

Balloon-Borne Hard X-Ray Imaging and Future Surveys

Several payloads for hard X-ray (20-600 keV) imaging with coded aperture telescopes have been developed for balloon flight observations of cosmic x-ray sources. We briefly review the characteristics of these, particularly the EXITE2 system. The recent NASA program to develop an extended long duration (100d) balloon flight capability employing super-pressure balloons would allow a qualitatively new hard x-ray imaging experiment: the Energetic X-ray Imaging Survey Telescope-Long Integration Time Experiment (EXIST-LITE). The longer continuous viewing times (per source) available from an LDB platform than from low earth orbit would enable both surveys and objectives complementary to the EXIST mission proposed for a MIDEX satellite. We summarize the scientific objectives of EXIST-LITE, a possible instrumentation approach incorporating a large area array of Cd-Zn-Te (CZT) detectors, and our program for the development and balloon flight testing of relatively thick (5mm) CZT detector arrays.Comment: 10 pages Latex and includes 3 figures (postscript). Invited talk at COSPAR (Birmingham, UK; July 96); to appear in Adv. in Sp. Res. (1998

Chemical Compatibility Testing Final Report Including Test Plans and Procedures

This report provides an independent assessment of information on mixed waste streams, chemical compatibility information on polymers, and standard test methods for polymer properties. It includes a technology review of mixed low-level waste (LLW) streams and material compatibilities, validation for the plan to test the compatibility of simulated mixed wastes with potential seal and liner materials, and the test plan itself. Potential packaging materials were reviewed and evaluated for compatibility with expected hazardous wastes. The chemical and physical property measurements required for testing container materials were determined. Test methodologies for evaluating compatibility were collected and reviewed for applicability. A test plan to meet US Department of Energy and Environmental Protection Agency requirements was developed. The expected wastes were compared with the chemical resistances of polymers, the top-ranking polymers were selected for testing, and the most applicable test methods for candidate seal and liner materials were determined. Five recommended solutions to simulate mixed LLW streams are described. The test plan includes descriptions of test materials, test procedures, data collection protocols, safety and environmental considerations, and quality assurance procedures. The recommended order of testing to be conducted is specified