Integrable system on minimal nilpotent orbit

Math Phys Anal Geom 27, 18 (2024) We show that for every complex simple Lie algebra, the equations of Schubert divisors on the flag variety give a complete integrable system of the minimal nilpotent orbit. The approach is motivated by the integrable system on Coulomb branch. We give explicit computa...

Full description

Saved in:

Bibliographic Details
Main Author:	Tu, Xinyue
Format:	Journal Article
Language:	English
Published:	25-09-2024
Subjects:	Mathematics - Algebraic Geometry Mathematics - Mathematical Physics Mathematics - Representation Theory Physics - Mathematical Physics
Online Access:	Get full text
Tags:	Add Tag No Tags, Be the first to tag this record!

Description
Summary:	Math Phys Anal Geom 27, 18 (2024) We show that for every complex simple Lie algebra, the equations of Schubert divisors on the flag variety give a complete integrable system of the minimal nilpotent orbit. The approach is motivated by the integrable system on Coulomb branch. We give explicit computations of these Hamiltonian functions, using Chevalley basis and a so-called Heisenberg algebra basis. For classical Lie algebras we rediscover the lower order terms of the celebrated Gelfand-Zeitlin system. For exceptional types we computed the number of Hamiltonian functions associated to each vertex of Dynkin diagram. They should be regarded as analogs of Gelfand-Zeitlin functions on exceptional type Lie algebras.
DOI:	10.48550/arxiv.2408.13020