On a relative version of Serre's notion of G-complete reducibility

Abstract: We first review some basic results related to Serre's notion of G-complete reducibility for a reductive algebraic group G. We then discuss a relative variant of this concept where we let K be a reductive subgroup of G, and consider subgroups of G which normalise the identity component $K^\circ$ of K. We show that such a subgroup is relatively G-completely reducible with respect to K if and only if its image in the automorphism group of $K^\circ$ is completely reducible in the sense of Serre. This allows us to generalise a number of fundamental results from the absolute to the relative setting. This is a report on recent joint work with M. Gruchot and A. Litterick.

algebraic geometryalgebraic topologycomplex variablesdifferential geometrygeometric topologymetric geometryquantum algebrarepresentation theory

Audience: researchers in the topic

Sapienza A&G Seminar

Series comments: Weekly research seminar in algebra and geometry.

"Sapienza" Università di Roma, Department of Mathematics "Guido Castelnuovo".