Seminar talk, 11 October 2017

From Geometry of Differential Equations
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Speaker: Pavel Bibikov

Title: Irreducible representations of semisimple algebraic groups from differential point of view

In this talk we discuss an approach to the study of orbits of actions of semisimple algebraic groups in their irreducible complex representations, which is based on differential invariants on the one hand, and on geometry of reductive homogeneous spaces on the other hand. According to the Borel-Weil-Bott theorem, every irreducible representation of semisimple Lie group is isomorphic to the action of this group on the module of holomorphic sections of some one-dimensional bundle over homogeneous space. Using this, we give a complete description of the structure of the field of differential invariants for this action and obtain a criterion which separates regular orbits.

In collaboration with Valentin Lychagin.