Integrable system on minimal nilpotent orbit

Autor:	Tu, Xinyue
Rok vydání:	2024
Předmět:	Mathematics - Algebraic Geometry Mathematical Physics Mathematics - Representation Theory 17B80 17B08 17B63 22E46 14D21
Zdroj:	Math Phys Anal Geom 27, 18 (2024)
Druh dokumentu:	Working Paper
DOI:	10.1007/s11040-024-09489-6
Popis:	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. Comment: 23 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2408.13020 Zobrazit plný text záznamu View this record from Arxiv