112 citations · 131 across the 13 of their papers we have counts for
25 papers
Complete reducibility for Lie subalgebras and semisimplification
Michael Bate, Sören Böhm, Benjamin Martin +2
Let be a connected reductive linear algebraic group over a field . Using ideas from geometric invariant theory, we study the notion of -complete reducibility over for…
Overgroups of regular unipotent elements in reductive groups
Michael Bate, Ben Martin, Gerhard Roehrle
We study reductive subgroups of a reductive linear algebraic group -- possibly non-connected -- such that contains a regular unipotent element of . We show that unde…
Semisimplification for Subgroups of Reductive Algebraic Groups
Michael Bate, Benjamin Martin, Gerhard Roehrle
Let be a reductive algebraic group---possibly non-connected---over a field and let be a subgroup of . If then there is a degeneration process for obtaining…
Cutoff for a One-sided Transposition Shuffle
Michael E. Bate, Stephen B. Connor, Oliver Matheau-Raven
We introduce a new type of card shuffle called one-sided transpositions. At each step a card is chosen uniformly from the pack and then transposed with another card chosen uniforml…
On relative complete reducibility
Christopher Attenborough, Michael Bate, Maike Gruchot +2
Let be a reductive subgroup of a reductive group over an algebraically closed field . The notion of relative complete reducibility, introduced in previous work of Bate-M…
Irreducible modules for pseudo-reductive groups
Michael Bate, David I. Stewart
We classify the irreducible representations of smooth, connected affine algebraic groups over a field, by tackling the case of pseudo-reductive groups. We reduce the problem of cal…