Sandwich operators and Einstein deformations of compact symmetric spaces related to Jordan algebras

Autor:	Hall, Stuart James, Schwahn, Paul, Semmelmann, Uwe
Rok vydání:	2024
Předmět:	Mathematics - Differential Geometry Mathematics - Rings and Algebras 17B20 17B60 53C24 53C25 53C35
Druh dokumentu:	Working Paper
Popis:	We study the deformability of the symmetric Einstein metrics on the spaces $\mathrm{SU}(n)/\mathrm{SO}(n)$ and $\mathrm{SU}(2n)/\mathrm{Sp}(n)$, thereby concluding the problem to second order for all irreducible symmetric spaces. The obstruction integrals are calculated from invariant polynomials on certain Lie algebra representations. To aid the computation, we develop so-called sandwich operators for compact Lie algebras and relate them to quadratic Casimir operators. We also explain the source of the infinitesimal Einstein deformations on irreducible symmetric spaces, except for the complex Grassmannians, by exploring their relation to simple Jordan algebras. As an application we prove the nonlinear instability of most of the infinitesimally deformable irreducible compact symmetric spaces. Comment: 34 pages, comments welcome
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2412.08770 Zobrazit plný text záznamu View this record from Arxiv