Let G be a simply connected semisimple algebraic group with Lie algebra g, let G0 ⊂ G be the symmetric subgroup defined by an algebraic involution σ and let g1 ⊂ g be the isotropy representation of G0. Given an abelian subalgebra a of g contained in g1 and stable under the action of some Borel subgroup B0 ⊂ G0, we classify the B0-orbits in a and characterize the sphericity of G0a. Our main tool is the combinatorics of σ-minuscule elements in the affine Weyl group of g and that of strongly orthogonal roots in Hermitian symmetric spaces.

Spherical nilpotent orbits and abelian subalgebras in isotropy representations / Gandini, Jacopo; Frajria, Pierluigi M¨oseneder; Papi, Paolo. - In: JOURNAL OF THE LONDON MATHEMATICAL SOCIETY. - ISSN 0024-6107. - STAMPA. - 95:(2017), pp. 323-352. [10.1112/jlms.12022]

Spherical nilpotent orbits and abelian subalgebras in isotropy representations

PAPI, Paolo
2017

Abstract

Let G be a simply connected semisimple algebraic group with Lie algebra g, let G0 ⊂ G be the symmetric subgroup defined by an algebraic involution σ and let g1 ⊂ g be the isotropy representation of G0. Given an abelian subalgebra a of g contained in g1 and stable under the action of some Borel subgroup B0 ⊂ G0, we classify the B0-orbits in a and characterize the sphericity of G0a. Our main tool is the combinatorics of σ-minuscule elements in the affine Weyl group of g and that of strongly orthogonal roots in Hermitian symmetric spaces.
2017
Spherical orbit; nilpotent orbit; abelian subalgefbras; isotropy representation
01 Pubblicazione su rivista::01a Articolo in rivista
Spherical nilpotent orbits and abelian subalgebras in isotropy representations / Gandini, Jacopo; Frajria, Pierluigi M¨oseneder; Papi, Paolo. - In: JOURNAL OF THE LONDON MATHEMATICAL SOCIETY. - ISSN 0024-6107. - STAMPA. - 95:(2017), pp. 323-352. [10.1112/jlms.12022]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/924939
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