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

University of Haifa

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	American 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

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1016/j.crma.2011.05.016

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title = "On geometric properties of orbital varieties in type A",

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",

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.",

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language = "American English",

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AU - Fresse, Lucas

AU - Melnikov, Anna

N1 - Funding Information: E-mail addresses: [email protected] (L. Fresse), [email protected] (A. Melnikov). 1 Supported by the European project GLC, ERC grant No. 247049.

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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.

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DO - 10.1016/j.crma.2011.05.016

M3 - Article

SN - 1631-073X

VL - 349

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EP - 739

JO - Comptes Rendus Mathematique

JF - Comptes Rendus Mathematique

IS - 13-14

ER -

On geometric properties of orbital varieties in type A

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