The null-cone and cohomology of vector bundles on flag varieties

Vilonen, Kari; Xue, Ting

doi:10.1090/ert/491

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The null-cone and cohomology of vector bundles on flag varieties

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Vilonen, Kari
Max Planck Institute for Mathematics, Max Planck Society;

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Xue, Ting
Max Planck Institute for Mathematics, Max Planck Society;

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Vilonen-Xue_The null-cone and cohomology of vector bundles on flag varieties_2016.pdf
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Vilonen, K., & Xue, T. (2016). The null-cone and cohomology of vector bundles on flag varieties. Representation Theory, 20, 482-498. doi:10.1090/ert/491.

Cite as: https://hdl.handle.net/21.11116/0000-0004-6C8C-6

Abstract

We study the null-cone of a semi-simple algebraic group acting on a number of copies of its Lie algebra via the diagonal adjoint action. We show that the null-cone has rational singularities in the case of $SL_3$.We observe by example that the null-cone is not normal in general and that the normalization of the null-cone does not have rational singularities in general. This is achieved by computing cohomology of certain vector bundles on flag varieties.