Displaying similar documents to “Limit formulas for groups with one conjugacy class of Cartan subgroups”

Constant term in Harish-Chandra’s limit formula

Mladen Božičević (2008)

Annales mathématiques Blaise Pascal

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Let G ℝ be a real form of a complex semisimple Lie group G . Recall that Rossmann defined a Weyl group action on Lagrangian cycles supported on the conormal bundle of the flag variety of G . We compute the signed average of the Weyl group action on the characteristic cycle of the standard sheaf associated to an open G ℝ -orbit on the flag variety. This result is applied to find the value of the constant term in Harish-Chandra’s limit formula for the delta function at zero.

Smooth components of Springer fibers

William Graham, R. Zierau (2011)

Annales de l’institut Fourier

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This article studies components of Springer fibers for 𝔤𝔩 ( n ) that are associated to closed orbits of G L ( p ) × G L ( q ) on the flag variety of G L ( n ) , n = p + q . These components occur in any Springer fiber. In contrast to the case of arbitrary components, these components are smooth varieties. Using results of Barchini and Zierau we show these components are iterated bundles and are stable under the action of a maximal torus of G L ( n ) . We prove that if ℒ is a line bundle on the flag variety associated to a dominant weight,...

Linear maps preserving orbits

Gerald W. Schwarz (2012)

Annales de l’institut Fourier

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Let H ⊂ GL ( V ) be a connected complex reductive group where V is a finite-dimensional complex vector space. Let v ∈ V and let G = { g ∈ GL ( V ) ∣ g H v = H v } . Following Raïs we say that the orbit H v is if the identity component of G is H . If H is semisimple, we say that H v is for H if the identity component of G is an extension of H by a torus. We classify the H -orbits which are not (semi)-characteristic in many cases.

Surprising properties of centralisers in classical Lie algebras

Oksana Yakimova (2009)

Annales de l’institut Fourier

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Let 𝔤 be a classical Lie algebra, , either 𝔤𝔩 n , 𝔰𝔭 n , or 𝔰𝔬 n and let e be a nilpotent element of 𝔤 . We study various properties of the centralisers 𝔤 e . The first four sections deal with rather elementary questions, like the centre of 𝔤 e , commuting varieties associated with 𝔤 e , or centralisers of commuting pairs. The second half of the paper addresses problems related to different Poisson structures on 𝔤 e * and symmetric invariants of 𝔤 e .

Orbit functions.

Klimyk, Anatoliy, Patera, Jiri (2006)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

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