On intersections of orbital varieties and components of Springer fiber

A. Melnikov; N. Gioan J. Pagnon

doi:10.1016/j.jalgebra.2006.01.029

On intersections of orbital varieties and components of Springer fiber

A. Melnikov, N. Gioan J. Pagnon

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We consider Springer fibers and orbital varieties for GL_n. We show that the irreducible components of an intersection of components of Springer fiber are in bijection with the irreducible components of intersection of orbital varieties; moreover, the corresponding irreducible components in this correspondence have the same codimension. Finally we give a sufficient condition to have an intersection in codimension one.

Original language	English
Pages (from-to)	1-14
Number of pages	14
Journal	Journal of Algebra
Volume	298
Issue number	1
DOIs	https://doi.org/10.1016/j.jalgebra.2006.01.029
State	Published - 1 Apr 2006

Bibliographical note

Funding Information:
* Corresponding author. E-mail addresses: [email protected] (A. Melnikov), [email protected] (N.G.J. Pagnon). 1 Supported in part by the Marie Curie Research Training Network “Liegrits.” 2 The author is supported by the Feinberg Graduate School fellowship and the Marie Curie Research Training Network “Liegrits.” 0021-8693/$ – see front matter  2006 Elsevier Inc. All rights reserved. doi:10.1016/j.jalgebra.2006.01.029

Keywords

Flag manifold
Orbital varieties
Robinson-Schensted correspondence
Schubert cell
Springer fibers

ASJC Scopus subject areas

Algebra and Number Theory

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10.1016/j.jalgebra.2006.01.029

Cite this

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title = "On intersections of orbital varieties and components of Springer fiber",

abstract = "We consider Springer fibers and orbital varieties for GLn. We show that the irreducible components of an intersection of components of Springer fiber are in bijection with the irreducible components of intersection of orbital varieties; moreover, the corresponding irreducible components in this correspondence have the same codimension. Finally we give a sufficient condition to have an intersection in codimension one.",

keywords = "Flag manifold, Orbital varieties, Robinson-Schensted correspondence, Schubert cell, Springer fibers",

author = "A. Melnikov and Pagnon, {N. Gioan J.}",

note = "Funding Information: * Corresponding author. E-mail addresses: [email protected] (A. Melnikov), [email protected] (N.G.J. Pagnon). 1 Supported in part by the Marie Curie Research Training Network “Liegrits.” 2 The author is supported by the Feinberg Graduate School fellowship and the Marie Curie Research Training Network “Liegrits.” 0021-8693/$ – see front matter  2006 Elsevier Inc. All rights reserved. doi:10.1016/j.jalgebra.2006.01.029",

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AU - Melnikov, A.

AU - Pagnon, N. Gioan J.

N1 - Funding Information: * Corresponding author. E-mail addresses: [email protected] (A. Melnikov), [email protected] (N.G.J. Pagnon). 1 Supported in part by the Marie Curie Research Training Network “Liegrits.” 2 The author is supported by the Feinberg Graduate School fellowship and the Marie Curie Research Training Network “Liegrits.” 0021-8693/$ – see front matter  2006 Elsevier Inc. All rights reserved. doi:10.1016/j.jalgebra.2006.01.029

PY - 2006/4/1

Y1 - 2006/4/1

N2 - We consider Springer fibers and orbital varieties for GLn. We show that the irreducible components of an intersection of components of Springer fiber are in bijection with the irreducible components of intersection of orbital varieties; moreover, the corresponding irreducible components in this correspondence have the same codimension. Finally we give a sufficient condition to have an intersection in codimension one.

AB - We consider Springer fibers and orbital varieties for GLn. We show that the irreducible components of an intersection of components of Springer fiber are in bijection with the irreducible components of intersection of orbital varieties; moreover, the corresponding irreducible components in this correspondence have the same codimension. Finally we give a sufficient condition to have an intersection in codimension one.

KW - Flag manifold

KW - Orbital varieties

KW - Robinson-Schensted correspondence

KW - Schubert cell

KW - Springer fibers

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DO - 10.1016/j.jalgebra.2006.01.029

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EP - 14

JO - Journal of Algebra

JF - Journal of Algebra

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ER -

On intersections of orbital varieties and components of Springer fiber

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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