Extensions of the Toda system via Hessenberg varieties and Slodowy slices (Peter Crooks ,Hausdorff research institute at Hannover)

29.01.2018 15:30

Toda systems and related integrable systems have been studied at the interface of algebraic geometry, holomorphic symplectic geometry, and representation theory. One instance of this involves fixing a complex semisimple algebraic group G with Borel subgroup B, in which setting Kostant studied the Toda system on a coadjoint B-orbit.

I will discuss embeddings of Kostant's Toda system into integrable systems on two larger varieties. The first of these varieties will be a holomorphic symplectic variety constructed via Slodowy slices, while the second will be a certain well-studied family of Hessenberg varieties. If time permits, I will discuss some implications of the two embeddings.

This represents previous work with S. Rayan and ongoing work with H. Abe.

Lieu

Bâtiment: Battelle

Séminaire "Groupes de Lie et espaces des modules"

entrée libre