On geometric properties of orbital varieties in type A

Lucas Fresse; Anna Melnikov

doi:10.1016/j.crma.2011.05.016

On geometric properties of orbital varieties in type A

Lucas Fresse
, Anna Melnikov

Department of Mathematics

Research output: Contribution to journal › Article › peer-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 language	English
Pages (from-to)	735-739
Number of pages	5
Journal	Comptes Rendus Mathematique
Volume	349
Issue number	13-14
DOIs	https://doi.org/10.1016/j.crma.2011.05.016
State	Published - Jul 2011

Bibliographical note

Funding Information:
E-mail addresses: [email protected] (L. Fresse), [email protected] (A. Melnikov). 1 Supported by the European project GLC, ERC grant No. 247049.

ASJC Scopus subject areas

General Mathematics

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10.1016/j.crma.2011.05.016

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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.",

author = "Lucas Fresse and Anna Melnikov",

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N2 - 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.

AB - 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.

UR - https://www.scopus.com/pages/publications/80051556891

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ER -

On geometric properties of orbital varieties in type A

Abstract

Bibliographical note

ASJC Scopus subject areas

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