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- W2073663922 abstract "Let $G$ be a Lie group, $H$ a closed subgroup and $M$ the homogeneous space $G/H$. Each representation $Psi$ of $H$ determines a $G$-equivariant principal bundle ${mathcal P}$ on $M$ endowed with a $G$-invariant connection. We consider subgroups ${mathcal G}$ of the diffeomorphism group ${rm Diff}(M)$, such that, each vector field $Zin{rm Lie}({mathcal G})$ admits a lift to a preserving connection vector field on ${mathcal P}$. We prove that $#,pi_1({mathcal G})geq #,Psi(Z(G))$. This relation is applicable to subgroups ${mathcal G}$ of the Hamiltonian groups of the flag varieties of a semisimple group $G$. Let $M_{Delta}$ be the toric manifold determined by the Delzant polytope $Delta$. We put $varphi_{bf b}$ for the the loop in the Hamiltonian group of $M_{Delta}$ defined by the lattice vector ${bf b}$. We give a sufficient condition, in terms of the mass center of $Delta$, for the loops $varphi_{bf b}$ and $varphi_{bftilde b}$ to be homotopically inequivalent." @default.
- W2073663922 created "2016-06-24" @default.
- W2073663922 creator A5090967322 @default.
- W2073663922 date "2013-10-08" @default.
- W2073663922 modified "2023-09-25" @default.
- W2073663922 title "LIFTING HAMILTONIAN LOOPS TO ISOTOPIES IN FIBRATIONS" @default.
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- W2073663922 doi "https://doi.org/10.1142/s0219887813500576" @default.
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