Complements on disconnected reductive groups

We present various results on disconnected reductive groups, in particular about the characteristic 0 representation theory of such groups over finite fields.Comment: This version takes into account improvements suggested by G. Mall

The space of unipotently supported class functions on a finite reductive group

We determine the Lusztig restrictions on the space of class functions with a unipotent support on a finite reductive group. In particular we give a simple expression for the Lusztig restrictions of the generalized Green functions and we describe the Lusztig restrictions of the generalized Gelfand-Graev representations. We make explicit computations for the Gelfand-Graev representations associated to the subregular unipotent class. In the case of SLn we show that the computations can be reduced to the case of GLn' for various n'.Comment: 21 page

Parabolic Deligne-Lusztig varieties

Motivated by the Brou\'e conjecture on blocks with abelian defect groups for finite reductive groups, we study "parabolic" Deligne-Lusztig varieties and construct on those which occur in the Brou\'e conjecture an action of a braid monoid, whose action on their $\ell$-adic cohomology will conjecturally factor trough a cyclotomic Hecke algebra. In order to construct this action, we need to enlarge the set of varieties we consider to varieties attached to a "ribbon category"; this category has a {\em Garside family}, which plays an important role in our constructions, so we devote the first part of our paper to the necessary background on categories with Garside families

Lake Kivu Water Chemistry Variation with Depth Over Time, Northwestern Rwanda

The water of East African rift lakes contains large amounts of dissolved chemicals such as carbon dioxide, methane greatly and others like  phosphate, silicate, Sulfate, Sulfide, Iron, Ammonia, Alkalinity etc. Lake Kivu is a large, deep rift basin lake located in the western branch of the East African rift zone that contains a methane gas deposit of great economic interest with two main sources: Inorganic carbon dioxide CO2 + 4H2 = CH4 + 2H2O and Organic methanogenesis CH3COOH =CH4 + CO2. Lake Kivu is a stratified, meromictic lake bordering Rwanda and the Democratic Republic of the Congo (DRC). The lake has a surface area of 2,370 Km2, a volume of 580 Km3 and a maximum water depth of 485 m. To characterize the vertical variation of Lake Kivu water chemistry, 8 samples of water were collected using Niskin bottles in Lake Kivu near Gisenyi town. Water samples were therefore collected at different depths: 0 m, 40 m, 90 m, 240 m, 290 m, 340 m, 340 m, and 390 m. Hatch kits were used to analyze  water chemistry of samples taken of Sulfate, Sulfide, Iron, Ammonia, Alkalinity, Silica, PO4,andphosphorus.The results revealed that alkalinity  increases in the monimolimnion part due to the precipitation of calcium carbonate in the upper levels of the water column and dissolution in the monimolimnion. The conductivity, dissolved oxygen, temperature and pH weremeasured by CTD Sonde. Water column data from these studies showed increasing concentrations with depth. The divide between the mixolimnion and monomolimnion is estimated at a depth of around 40 m. Higher amounts of silica observed closer to the shoreline is likely a result of an influx of siliciclastic sediment and increased silica with depth is likely a result of the dissolution of diatoms below the photic zone. Keywords: Monimolimnion, mixolimnion, water stratification, chemicals agents

Irreducible characters of GSp(4, q) and dimensions of spaces of fixed vectors

In this paper, we compute the conjugacy classes and the list of irreducible characters of GSp(4,q), where q is odd. We also determine precisely which irreducible characters are non-cuspidal and which are generic. These characters are then used to compute dimensions of certain subspaces of fixed vectors of smooth admissible non-supercuspidal representations of GSp(4,F), where F is a non-archimedean local field of characteristic zero with residue field of order q.Comment: 48 pages, 21 tables. Corrected an error in Table 16 for type V* representations (theta_11 and theta_12 were switched

The supercuspidal representations of p-adic classical groups

Let G be a unitary, symplectic or special orthogonal group over a locally compact non-archimedean local field of odd residual characteristic. We construct many new supercuspidal representations of G, and Bushnell-Kutzko types for these representations. Moreover, we prove that every irreducible supercuspidal representation of G arises from our constructions.Comment: 55 pages -- minor changes from 1st version (mostly in sections 2.2, 4.2 and 6.2). To appear in Inventiones mathematicae, 2008 (DOI is not yet active as at 12 Nov 2007

On the elliptic nonabelian Fourier transform for unipotent representations of p-adic groups

In this paper, we consider the relation between two nonabelian Fourier transforms. The first one is defined in terms of the Langlands-Kazhdan-Lusztig parameters for unipotent elliptic representations of a split p-adic group and the second is defined in terms of the pseudocoefficients of these representations and Lusztig's nonabelian Fourier transform for characters of finite groups of Lie type. We exemplify this relation in the case of the p-adic group of type G_2.Comment: 17 pages; v2: several minor corrections, references added; v3: corrections in the table with unipotent discrete series of G

The structure of blocks with a Klein four defect group

We prove Erdmann’s conjecture [16] stating that every block with a Klein four defect group has a simple module with trivial source, and deduce from this that Puig’s finiteness conjecture holds for source algebras of blocks with a Klein four defect group. The proof uses the classification of finite simple groups

Determining adsorbate configuration on alumina surfaces with 13C nuclear magnetic resonance relaxation time analysis

Relative strengths of surface interaction for individual carbon atoms in acyclic and cyclic hydrocarbons adsorbed on alumina surfaces are determined using chemically resolved 13C nuclear magnetic resonance (NMR) T1 relaxation times. The ratio of relaxation times for the adsorbed atoms T1,ads to the bulk liquid relaxation time T1,bulk provides an indication of the mobility of the atom. Hence a low T1,ads/T1,bulk ratio indicates a stronger surface interaction. The carbon atoms associated with unsaturated bonds in the molecules are seen to exhibit a larger reduction in T1 on adsorption relative to the aliphatic carbons, consistent with adsorption occurring through the carbon-carbon multiple bonds. The relaxation data are interpreted in terms of proximity of individual carbon atoms to the alumina surface and adsorption conformations are inferred. Furthermore, variations of interaction strength and molecular configuration have been explored as a function of adsorbate coverage, temperature, surface pre-treatment, and in the presence of co-adsorbates. This relaxation time analysis is appropriate for studying the behaviour of hydrocarbons adsorbed on a wide range of catalyst support and supported-metal catalyst surfaces, and offers the potential to explore such systems under realistic operating conditions when multiple chemical components are present at the surface