{Twisted Poincar\'e Series and Geometric Factorization of Affine Weyl Groups

We study the relation between the alternating product of twisted Poincar'e series of parabolic subgroups of affine Weyl groups and hyperbolic stabilizers of geodesic tubes. Moreover, from such relation, we find a length-preserving factorization of affine Weyl groups of type $\tilde{A}_n$ and $\tilde{C}_n$

On finite group actions on reductive groups and buildings

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On quasi-reductive group schemes

The paper was motivated by a question of Vilonen, and the main results have been used by Mirkovic and Vilonen to give a geometric interpretation of the dual group (as a Chevalley group over Z) of a reductive group. We define a quasi-reducitve group over a discrete valuation ring R to be an affine flat group scheme over R such that (i) the fibers are of finite type and of the same dimension; (ii) the generic fiber is smooth and connected, and (iii) the netural component of the reduced special fiber is a reductive group. We show that such a group scheme is of finite type over R, the generic fiber is a reductive group, the special fiber is connected, and the group scheme is smooth over R in most cases, for example when the residue characteristic is not 2, or when the generic fiber and reduced special fiber are of the same type as reductive groups. We also obtain results about group schemes over a Dedekind scheme or a noetherian scheme. We show that in residue characteristic 2 there are indeed non-smooth quasi-reductive groups and they can be classified when R is strictly henselian

Twisted Levi Sequences and Explicit Styles on Sp(4)

Let G be a connected reductive group over a field F. A twisted Levi subgroup G0 of G is a reductive subgroup such that G' [circle times]F F[over-bar] is a Levi subgroup of G' [circle times]F F[over-bar]. Twisted Levi subgroups have been an important tool in studying the structure theory of representations of p-adic groups. For example, supercuspidal representations are built out of certain representations of twisted Levi subgroups ([20]), and Hecke algebra isomorphisms are established with Hecke algebras on twisted Levi subgroups, which suggests an inductive structure of representations (see [9] for example).National Science Foundation (U.S.). Focused Research Grou

Cavitation erosion of cast iron diesel engine liners

Photomicrographs from vibratory facility cavitation specimens and from an eroded liner of a field diesel engine are compared. The causes of erosion are similar. Corrosion tests show that the results are different from those from cavitation. This further confirms that liner erosion of a diesel engine is primarily due to cavitation erosion caused, in most cases, by vibration of the liner wall.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/24050/1/0000300.pd