Nilpotent orbits over ground fields of good characteristic

Let X be an F-rational nilpotent element in the Lie algebra of a connected and reductive group G defined over the ground field F. Suppose that the Lie algebra has a non-degenerate invariant bilinear form. We show that the unipotent radical of the centralizer of X is F-split. This property has several consequences. When F is complete with respect to a discrete valuation with either finite or algebraically closed residue field, we deduce a uniform proof that G(F) has finitely many nilpotent orbits in Lie(G)(F). When the residue field is finite, we obtain a proof that nilpotent orbital integrals converge. Under some further (fairly mild) assumptions on G, we prove convergence for arbitrary orbital integrals on the Lie algebra and on the group. The convergence of orbital integrals in the case where F has characteristic 0 was obtained by Deligne and Ranga Rao (1972).Comment: 32 pages, AMSLaTeX. To appear: Math. Annalen. This version has a new title; it also contains various corrections of typographic errors and such. More significantly, it contains "cleaner" statements of convergence for unipotent (as opposed to nilpotent) orbital integrals; see sections 8.5-8.

A survey of business concerns' attitude concerning sponsorship of educational television programs

Thesis (Ed.M.)--Boston Universit

Completely reducible Lie subalgebras

Let G be a connected and reductive group over the algebraically closed field K. J-P. Serre has introduced the notion of a G-completely reducible subgroup H of G. In this note, we give a notion of G-complete reducibility -- G-cr for short -- for Lie subalgebras of Lie(G), and we show that if the closed subgroup H < G is G-cr, then Lie(H) is G-cr as well.Comment: 7 pages; AMS LaTeX. To appear in *Transformation Groups

Analytic slowing-down distributions as modified by turbulent transport

The effect of electrostatic microturbulence on fast particles rapidly decreases at high energy, but can be significant at moderate energy. Previous studies found that, in addition to changes in the energetic particle density, this results in nontrivial changes to the equilibrium velocity distribution. These effects have implications for plasma heating and the stability of Alfv\'en eigenmodes, but make multiscale simulations much more difficult without further approximations. Here, several related analytic model distribution functions are derived from first principles with reasonable approximations. A single dimensionless parameter characterizes the relative strength of turbulence relative to collisions, and this parameter appears as an exponent in the model distribution functions. Even the most simple of these models reproduces key features of the numerical phase-space transport solution and provides a useful a priori heuristic for determining how strong the effect of turbulence is on the redistribution of energetic particles in toroidal plasmas.Comment: 13 pages; 6 figure

Dutch Treat

In the February 1976 Word Ways, Harry Mathews listed more than 250 French words which looked like English words but in reality had entirely different meanings. Here is an analogous list of Dutch words in English dress

Sub-principal homomorphisms in positive characteristic

Let G be a reductive group over an algebraically closed field of characteristic p, and let u in G be a unipotent element of order p. Suppose that p is a good prime for G. We show in this paper that there is a homomorphism phi:SL_2/k --> G whose image contains u. This result was first obtained by D. Testerman (J. Algebra, 1995) using case considerations for each type of simple group (and using, in some cases, computer calculations with explicit representatives for the unipotent orbits). The proof we give is free of case considerations (except in its dependence on the Bala-Carter theorem). Our construction of phi generalizes the construction of a principal homomorphism made by J.-P. Serre in (Invent. Math. 1996); in particular, phi is obtained by reduction modulo P from a homomorphism of group schemes over a valuation ring in a number field. This permits us to show moreover that the weight spaces of a maximal torus of phi(SL_2/k) on Lie(G) are ``the same as in characteristic 0''; the existence of a phi with this property was previously obtained, again using case considerations, by Lawther and Testerman (Memoirs AMS, 1999) and has been applied in some recent work of G. Seitz (Invent. Math. 2000).Comment: 20 pages, AMS LaTeX. This version fixes some minor glitches, and includes a more detailed section 5.3. To appear in Math. Zeitschrif

A survey of business concerns' attitude concerning sponsorship of educational television programs

Thesis (Ed.M.)--Boston Universit

Centerscope

Centerscope, formerly Scope, was published by the Boston University Medical Center "to communicate the concern of the Medical Center for the development and maintenance of improved health care in contemporary society.