We define the class of rigid Frobenius algebras in a (non-semisimple) modular category and prove that their categories local modules are, again, modular. This generalizes previous work Kirillov Ostrik (Adv Math 171(2):183–227, 2002) semisimple setup. Examples non-semisimple via modules, as well connections to authors’ prior on relative monoidal centers, are provided. In particular, we classify ...

The classification of spherical varieties is already known for semisimple groups of types A and D. Adding type E, we complete the classification for all semisimple groups with a simply laced Dynkin diagram.

The Iwasawa decomposition of a connected semisimple complex Lie group or a connected semisimple split real Lie group is one of the most fundamental observations of classical Lie theory. It implies that the geometry of a connected semisimple complex resp. split real Lie group G is controlled by any maximal compact subgroup K. Examples are Weyl’s unitarian trick in the representation theory of Li...