Let G be a semisimple complex algebraic group, and H ⊆ G a wonderful subgroup. We prove several results relating the subgroup H to the properties of a combinatorial invariant S of G/H, called its spherical system. It is also possible to consider a spherical system S as a datum defined by purely combinatorial axioms, and under certain circumstances our results prove the existence of a wonderful subgroup H associated with S. As a byproduct, we reduce for any group G the proof of the classification of wonderful G-varieties, known as the Luna conjecture, to its verification on a small family of cases, called primitive. © 2014 Elsevier Inc.
Wonderful subgroups of reductive groups and spherical systems / Bravi, Paolo; Pezzini, Guido. - In: JOURNAL OF ALGEBRA. - ISSN 0021-8693. - STAMPA. - 409:(2014), pp. 101-147. [10.1016/j.jalgebra.2014.03.018]
Wonderful subgroups of reductive groups and spherical systems
BRAVI, Paolo;PEZZINI, Guido
2014
Abstract
Let G be a semisimple complex algebraic group, and H ⊆ G a wonderful subgroup. We prove several results relating the subgroup H to the properties of a combinatorial invariant S of G/H, called its spherical system. It is also possible to consider a spherical system S as a datum defined by purely combinatorial axioms, and under certain circumstances our results prove the existence of a wonderful subgroup H associated with S. As a byproduct, we reduce for any group G the proof of the classification of wonderful G-varieties, known as the Luna conjecture, to its verification on a small family of cases, called primitive. © 2014 Elsevier Inc.File | Dimensione | Formato | |
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