Isotropy irreducible spaces and s-representations
نویسندگان
چکیده
منابع مشابه
ISOTROPY IRREDUCIBLE SPACES AND s-REPRESENTATIONS
A simple description of isotropy irreducible spaces G/K is given when G is a classical compact Lie group and K is compact and connected.
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For an element x of the Cuntz algebra ON , define the isotropy subgroup Gx ≡ {g ∈ U(N) : αg(x) = x} of the unitary group U(N) with respect to the canonical action α of U(N) on ON . We have irreducible representations of the crossed product ONoGx by extending irreducible generalized permutative representations of ON and irreducible representation of Gx. ¿From this, the Peter-Weyl theorem for Gx ...
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We introduce a new construction, the isotropy groupoid, to organize the orbit data for split Γ-spaces. We show that equivariant principal G-bundles over split Γ-CW complexes X can be effectively classified by means of representations of their isotropy groupoids. For instance, if the quotient complex A = Γ\X is a graph, with all edge stabilizers toral subgroups of Γ, we obtain a purely combinato...
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A connected Riemannian manifold (M,g) is said to be isotropy irreducible if for each point p ∈ M the isotropy group Hp, i.e. all isometries of g fixing p, acts irreducibly on TpM via its isotropy representation. This class of manifolds is of great interest since they have a number of geometric properties which follow immediately from the definition. By Schur’s lemma the metric g is unique up to...
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ژورنال
عنوان ژورنال: Differential Geometry and its Applications
سال: 1996
ISSN: 0926-2245
DOI: 10.1016/0926-2245(96)89148-0