Algebra Seminar

Let G be a reductive algebraic group and let H be a reductive subgroup of G. Given h \in H, it is natural to ask whether the G-conjugacy class of h intersects H in a finite union of H-conjugacy classes. More generally, we can ask a similar question for an N-tuple h \in H^N.

I conjecture that the answer is yes. In this talk, I will present some supporting evidence, and discuss some applications of the conjecture.