Publications (8)
Closed Orbits and uniform S-instability in Geometric Invariant Theory
M. Bate, B. Martin, G. Roehrle +1
In this paper we consider various problems involving the action of a reductive group on an affine variety . We prove some general rationality results about the -orbits in…
Complete Reducibility and Commuting Subgroups
M. Bate, B. M. S. Martin, G. E. Roehrle
Let G be a reductive linear algebraic group over an algebraically closed field of characteristic p. We study J.-P. Serre's notion of G-complete reducibility for subgroups of G. In…
On Tits' Centre Conjecture for Fixed Point Subcomplexes
M. Bate, B. Martin, G. Roehrle
We give a short and uniform proof of a special case of Tits' Centre Conjecture using a theorem of J-P. Serre and a result from our earlier work. We consider fixed point subcomplexe…
Complete Reducibility and Conjugacy classes of tuples in Algebraic Groups and Lie algebras
M. Bate, B. Martin, G. Roehrle +1
Let H be a reductive subgroup of a reductive group G over an algebraically closed field k. We consider the action of H on G^n, the n-fold Cartesian product of G with itself, by sim…
Protostellar fragmentation in a power-law density distribution
A. Burkert, M. Bate, P. Bodenheimer
Hydrodynamical calculations in three space dimensions of the collapse of an isothermal, rotating 1 M\sol protostellar cloud are presented. The initial density stratification is a p…
Toward understanding the formation of multiple systems - A pilot IRAM-PdBI survey of Class 0 objects
A. J. Maury, Ph. Andre, P. Hennebelle +6
The formation process of binary stars and multiple systems is poorly understood. Here, we seek to determine the typical outcome of protostellar collapse and to constrain models of…
-complete reducibility and semisimple modules
M. Bate, S. Herpel, B. Martin +1
Let be a connected reductive algebraic group defined over an algebraically closed field % of characteristic . Our first aim in this note is to give concise and unifor…
A Geometric Approach to Complete Reducibility
M. Bate, B. M. S. Martin, G. Roehrle
Let G be a connected reductive linear algebraic group. We use geometric methods to investigate G-completely reducible subgroups of G, giving new criteria for G-complete reducibilit…