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Simplicity of Neretin's group of spheromorphisms

Christophe Kapoudjian (1999)

Annales de l'institut Fourier

Denote by 𝒯 n , n 2 , the regular tree whose vertices have valence n + 1 , 𝒯 n its boundary. Yu. A. Neretin has proposed a group N n of transformations of 𝒯 n , thought of as a combinatorial analogue of the diffeomorphism group of the circle. We show that N n is generated by two groups: the group Aut ( 𝒯 n ) of tree automorphisms, and a Higman-Thompson group G n . We prove the simplicity of N n and of a family of its subgroups.

Smooth components of Springer fibers

William Graham, R. Zierau (2011)

Annales de l’institut Fourier

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 is a line bundle on the flag variety associated to a dominant weight, then the higher...

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