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

Kari Vilonen, Ting Xue

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


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 SL3. 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.

Original languageEnglish (US)
Pages (from-to)482-498
Number of pages17
JournalRepresentation Theory
Issue number17
StatePublished - 2016

ASJC Scopus subject areas

  • Mathematics (miscellaneous)


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