Let G be a simply connected semisimple algebraic group with Lie algebra g, let G(0) subset of G be the symmetric subgroup defined by an algebraic involution sigma and let g(1) subset of g be the isotropy representation of G(0). Given an abelian subalgebra a of g contained in g(1) and stable under the action of some Borel subgroup B-0 subset of G(0), we classify the B-0-orbits in a and characterize the sphericity of G(0)a. Our main tool is the combinatorics of sigma-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 / J. Gandini, P. Möseneder Frajria, P. Papi. - In: JOURNAL OF THE LONDON MATHEMATICAL SOCIETY. - ISSN 0024-6107. - STAMPA. - 95:1(2017), pp. 323-352. [10.1112/jlms.12022]
Spherical nilpotent orbits and abelian subalgebras in isotropy representations
J. Gandini;P. Papi
2017
Abstract
Let G be a simply connected semisimple algebraic group with Lie algebra g, let G(0) subset of G be the symmetric subgroup defined by an algebraic involution sigma and let g(1) subset of g be the isotropy representation of G(0). Given an abelian subalgebra a of g contained in g(1) and stable under the action of some Borel subgroup B-0 subset of G(0), we classify the B-0-orbits in a and characterize the sphericity of G(0)a. Our main tool is the combinatorics of sigma-minuscule elements in the affine Weyl group of g and that of strongly orthogonal roots in Hermitian symmetric spaces.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.