Nijenhuis tensor and invariant polynomials

We discuss the diagonalization problem of the Nijenhuis tensor in a class of Poisson-Nijenhuis structures defined on compact hermitian symmetric spaces. We study its action on the ring of invariant polynomials of a Thimm chain of subalgebras. The existence of \(\phi\)-minimal representations defines...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2021-11
Main Authors: Bonechi, Francesco, Qiu, Jian, Tarlini, Marco, Viviani, Emanuele
Format: Article
Language:English
Subjects:
Invariants
Mathematical analysis
Polynomials
Representations
Rings (mathematics)
Tensors
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We discuss the diagonalization problem of the Nijenhuis tensor in a class of Poisson-Nijenhuis structures defined on compact hermitian symmetric spaces. We study its action on the ring of invariant polynomials of a Thimm chain of subalgebras. The existence of \(\phi\)-minimal representations defines a suitable basis of invariant polynomials that completely solves the diagonalization problem. We prove that such representations exist in the classical cases AIII, BDI, DIII and CI, and do not exist in the exceptional cases EIII and EVII. We discuss a second general construction that in these two cases computes partially the spectrum and hints at a different behavior with respect to the classical cases.
ISSN:2331-8422
DOI:10.48550/arxiv.2111.09769