Regular functions on spherical nilpotent orbits in complex symmetric pairs: Classical Hermitian cases
نویسندگان
چکیده
منابع مشابه
Rings of Regular Functions on Spherical Nilpotent Orbits for Complex Classical Groups
Let G be a classical group and let g be its Lie algebra. For a nilpotent element X E g, the ring R(Ox) of regular functions on the nilpotent orbit Ox is a Gmodule. In this thesis, we will decompose it into irreducible representations of G for some spherical nilpotent orbits. Thesis Supervisor: David Alexander Vogan Title: Professor of Mathematics
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Let G be the adjoint group of the simple real Lie algebra g , and let K C → Aut(p C ) be the complexified isotropy representation at the identity coset of the corresponding symmetric space. We classify the spherical nilpotent K C orbits in p C .
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τ(w)(x) = 〈x(w), w〉, w ∈ W, x ∈ g ⊆ End(W ), and similarly for τ ′. Our main theorem describes the behaviour of closures of nilpotent orbits under the action of moment maps. It is easy to see that for a nilpotent coadjoint orbit O ⊆ g∗ the set τ ′(τ−1(O)) is the union of nilpotent coadjoint orbits in g′. It turns out that it is a closure of a single orbit: Theorem 1.1 Let O ⊆ g∗ be a nilpotent ...
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We consider a reductive dual pair (G,G′) in the stable range with G′ the smaller member and of Hermitian symmetric type. We study the theta lifting of nilpotent K ′ C-orbits, where K ′ is a maximal compact subgroup of G′ and we describe the precise KC-module structure of the regular function ring of the closure of the lifted nilpotent orbit of the symmetric pair (G,K). As an application, we pro...
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Let G be a simple algebraic group defined over an algebraically closed field k of characteristic zero. Write g for its Lie algebra. Let x ∈ g be a nilpotent element and G·x ⊂ g the corresponding nilpotent orbit. The maximal number m such that (adx) 6= 0 is called the height of x or of G·x, denoted ht(x). Recall that an irreducible G-variety X is called G-spherical if a Borel subgroup of G has a...
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ژورنال
عنوان ژورنال: Kyoto Journal of Mathematics
سال: 2020
ISSN: 2156-2261
DOI: 10.1215/21562261-2019-0039