Let $G$ be a simply connected semisimple algebraic group with Lie algebra $mathfrak g$, let $G_0 subset G$ be the symmetric subgroup defined by an algebraic involution $sigma$ and let $mathfrak g_1 subset mathfrak g$ be the isotropy representation of $G_0$. Given an abelian subalgebra $mathfrak a$ of $mathfrak g$ contained in $mathfrak g_1$ and stable under the action of some Borel subgroup $B_0 subset G_0$, we classify the $B_0$-orbits in $mathfrak a$ and we characterize the sphericity of $G_0 mathfrak a$. Our main tool is the combinatorics of $sigma$-minuscule elements in the affine Weyl group of $mathfrak g$ and that of strongly orthogonal roots in Hermitian symmetric spaces.

Spherical nilpotent orbits and abelian subalgebras in isotropy representations

GANDINI, Jacopo;PAPI, PAOLO
2017

Abstract

Let $G$ be a simply connected semisimple algebraic group with Lie algebra $mathfrak g$, let $G_0 subset G$ be the symmetric subgroup defined by an algebraic involution $sigma$ and let $mathfrak g_1 subset mathfrak g$ be the isotropy representation of $G_0$. Given an abelian subalgebra $mathfrak a$ of $mathfrak g$ contained in $mathfrak g_1$ and stable under the action of some Borel subgroup $B_0 subset G_0$, we classify the $B_0$-orbits in $mathfrak a$ and we characterize the sphericity of $G_0 mathfrak a$. Our main tool is the combinatorics of $sigma$-minuscule elements in the affine Weyl group of $mathfrak g$ and that of strongly orthogonal roots in Hermitian symmetric spaces.
Settore MAT/03 - Geometria
Mathematics - Representation Theory; Mathematics - Representation Theory
File in questo prodotto:
File Dimensione Formato  
GMPfinal0727.pdf

Accesso chiuso

Tipologia: Accepted version (post-print)
Licenza: Non pubblico
Dimensione 505.24 kB
Formato Adobe PDF
505.24 kB Adobe PDF   Visualizza/Apri   Richiedi una copia

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11384/64501
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 2
  • ???jsp.display-item.citation.isi??? 2
social impact