On geometric properties of orbital varieties in type A

Lucas Fresse, Anna Melnikov

Research output: Contribution to journalArticlepeer-review

Abstract

The intersection between a nilpotent orbit O∪gln(C) and the Lie algebra Lie(B)∪gln(C) of a Borel subgroup B∪GLn(C) is an equidimensional, quasi-affine algebraic variety. Its irreducible components are called orbital varieties. In this Note, we provide criteria to guarantee that an orbital variety is smooth or has a dense orbit for the adjoint action of B. In addition, we point out a possible relation between these two properties.

Original languageEnglish
Pages (from-to)735-739
Number of pages5
JournalComptes Rendus Mathematique
Volume349
Issue number13-14
DOIs
StatePublished - Jul 2011

Bibliographical note

Funding Information:
E-mail addresses: lucasfresse@math.huji.ac.il (L. Fresse), melnikov@math.haifa.ac.il (A. Melnikov). 1 Supported by the European project GLC, ERC grant No. 247049.

ASJC Scopus subject areas

  • Mathematics (all)

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