Displaying similar documents to “Invariant differential operators on the tangent space of some symmetric spaces”

Cohomology of G / P for classical complex Lie supergroups G and characters of some atypical G -modules

Ivan Penkov, Vera Serganova (1989)

Annales de l'institut Fourier

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We compute the unique nonzero cohomology group of a generic G 0 - linearized locally free 𝒪 -module, where G 0 is the identity component of a complex classical Lie supergroup G and P ↪ G 0 is an arbitrary parabolic subsupergroup. In particular we prove that for G ≠ ℙ ( m ) , S ℙ ( m ) this cohomology group is an irreducible G 0 -module. As an application we generalize the character formula of typical irreducible G 0 -modules to a natural class of atypical modules arising in this way.

On the K -theory and Hattori-Stallings traces of minimal primitive factors of enveloping algebras of semisimple Lie algebras : the singular case

Patrick Polo (1995)

Annales de l'institut Fourier

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Let G be a semisimple complex algebraic group and X its flag variety. Let 𝔤 = Lie ( G ) and let U be its enveloping algebra. Let 𝔥 be a Cartan subalgebra of 𝔤 . For μ ∈ 𝔥 * , let J μ be the corresponding minimal primitive ideal, let U μ = U / J μ , and let 𝒯 U μ : K 0 ( U m u ) → ℂ be the Hattori-Stallings trace. Results of Hodges suggest to study this map as a step towards a classification, up to isomorphism or Morita equivalence, of the ℂ -algebras U μ . When μ is regular, Hodges has shown that K 0 ( U μ ) ≅ K 0 ( X ) . In this case K 0 ( U μ ) is generated by the classes corresponding...