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

Vilonen, Kari; Xue, Ting

doi:10.1090/ert/491

The null-cone and cohomology of vector bundles on flag varieties
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by Kari Vilonen and Ting Xue PDF

Represent. Theory 20 (2016), 482-498 Request permission

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.

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