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Invariant measure for some differential operators and unitarizing measure for the representation of a Lie group. Examples in finite dimension

Hélène Airault, Habib Ouerdiane (2011)

Banach Center Publications

Consider a Lie group with a unitary representation into a space of holomorphic functions defined on a domain 𝓓 of ℂ and in L²(μ), the measure μ being the unitarizing measure of the representation. On finite-dimensional examples, we show that this unitarizing measure is also the invariant measure for some differential operators on 𝓓. We calculate these operators and we develop the concepts of unitarizing measure and invariant measure for an OU operator (differential operator associated to...

Invariant prolongation of BGG-operators in conformal geometry

Matthias Hammerl (2008)

Archivum Mathematicum

BGG-operators form sequences of invariant differential operators and the first of these is overdetermined. Interesting equations in conformal geometry described by these operators are those for Einstein scales, conformal Killing forms and conformal Killing tensors. We present a deformation procedure of the tractor connection which yields an invariant prolongation of the first operator. The explicit calculation is presented in the case of conformal Killing forms.

Invariants homotopiques attachés aux fibrés symplectiques

Pierre Dazord (1979)

Annales de l'institut Fourier

On donne une construction géométrique d’invariants généralisant la classe de Maslov-Arnold d’une immersion lagrangienne dans un fibré cotangent et l’indice de Maslov-Arnold-Leray d’une immersion lagrangienne 2 q -orientée dans R n R n * : la classe de Maslov-Arnold universelle d’un fibré symplectique et l’indice de Maslov-Arnold-Leray d’un fibré q -symplectique, c’est-à-dire dont le groupe structural est le revêtement à q feuillets de S p ( n ) . Tout ceci relève d’une situation géométrique générale dans laquelle s’introduisent...

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