B-ORBITS OF SQUARE ZERO IN NILRADICAL OF THE SYMPLECTIC ALGEBRA

Nurit Barnea; Anna Melnikov

doi:10.1007/s00031-016-9401-x

B-ORBITS OF SQUARE ZERO IN NILRADICAL OF THE SYMPLECTIC ALGEBRA

Nurit Barnea, Anna Melnikov

Department of Mathematics

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

Abstract

Let Sp_2n(ℂ) be the symplectic group and [InlineMediaObject not available: see fulltext.](ℂ) its Lie algebra. Let B be a Borel subgroup of Sp_2n(ℂ), [InlineMediaObject not available: see fulltext.] = Lie(B) and [InlineMediaObject not available: see fulltext.] its nilradical. Let [InlineMediaObject not available: see fulltext.] be a subvariety of elements of square 0 in [InlineMediaObject not available: see fulltext.]: B acts adjointly on [InlineMediaObject not available: see fulltext.]. In this paper we describe the topology of orbits [InlineMediaObject not available: see fulltext.] in terms of symmetric link patterns. Further, we apply this description to the computations of the closures of orbital varieties of nilpotency order 2 and to their intersections. In particular, we show that all the intersections of codimension 1 are irreducible.

Original language	English
Pages (from-to)	885-910
Number of pages	26
Journal	Transformation Groups
Volume	22
Issue number	4
DOIs	https://doi.org/10.1007/s00031-016-9401-x
State	Published - 1 Dec 2017

Bibliographical note

Publisher Copyright:
© 2016, Springer Science+Business Media New York.

ASJC Scopus subject areas

Algebra and Number Theory
Geometry and Topology

Access to Document

10.1007/s00031-016-9401-x

Cite this

@article{3df2799a5dae4d3ca5887fdec97f8a13,

title = "B-ORBITS OF SQUARE ZERO IN NILRADICAL OF THE SYMPLECTIC ALGEBRA",

abstract = "Let Sp2n(ℂ) be the symplectic group and [InlineMediaObject not available: see fulltext.](ℂ) its Lie algebra. Let B be a Borel subgroup of Sp2n(ℂ), [InlineMediaObject not available: see fulltext.] = Lie(B) and [InlineMediaObject not available: see fulltext.] its nilradical. Let [InlineMediaObject not available: see fulltext.] be a subvariety of elements of square 0 in [InlineMediaObject not available: see fulltext.]: B acts adjointly on [InlineMediaObject not available: see fulltext.]. In this paper we describe the topology of orbits [InlineMediaObject not available: see fulltext.] in terms of symmetric link patterns. Further, we apply this description to the computations of the closures of orbital varieties of nilpotency order 2 and to their intersections. In particular, we show that all the intersections of codimension 1 are irreducible.",

author = "Nurit Barnea and Anna Melnikov",

note = "Publisher Copyright: {\textcopyright} 2016, Springer Science+Business Media New York.",

year = "2017",

month = dec,

day = "1",

doi = "10.1007/s00031-016-9401-x",

language = "English",

volume = "22",

pages = "885--910",

journal = "Transformation Groups",

issn = "1083-4362",

publisher = "Birkhauser Boston",

number = "4",

}

TY - JOUR

T1 - B-ORBITS OF SQUARE ZERO IN NILRADICAL OF THE SYMPLECTIC ALGEBRA

AU - Barnea, Nurit

AU - Melnikov, Anna

PY - 2017/12/1

Y1 - 2017/12/1

N2 - Let Sp2n(ℂ) be the symplectic group and [InlineMediaObject not available: see fulltext.](ℂ) its Lie algebra. Let B be a Borel subgroup of Sp2n(ℂ), [InlineMediaObject not available: see fulltext.] = Lie(B) and [InlineMediaObject not available: see fulltext.] its nilradical. Let [InlineMediaObject not available: see fulltext.] be a subvariety of elements of square 0 in [InlineMediaObject not available: see fulltext.]: B acts adjointly on [InlineMediaObject not available: see fulltext.]. In this paper we describe the topology of orbits [InlineMediaObject not available: see fulltext.] in terms of symmetric link patterns. Further, we apply this description to the computations of the closures of orbital varieties of nilpotency order 2 and to their intersections. In particular, we show that all the intersections of codimension 1 are irreducible.

AB - Let Sp2n(ℂ) be the symplectic group and [InlineMediaObject not available: see fulltext.](ℂ) its Lie algebra. Let B be a Borel subgroup of Sp2n(ℂ), [InlineMediaObject not available: see fulltext.] = Lie(B) and [InlineMediaObject not available: see fulltext.] its nilradical. Let [InlineMediaObject not available: see fulltext.] be a subvariety of elements of square 0 in [InlineMediaObject not available: see fulltext.]: B acts adjointly on [InlineMediaObject not available: see fulltext.]. In this paper we describe the topology of orbits [InlineMediaObject not available: see fulltext.] in terms of symmetric link patterns. Further, we apply this description to the computations of the closures of orbital varieties of nilpotency order 2 and to their intersections. In particular, we show that all the intersections of codimension 1 are irreducible.

UR - http://www.scopus.com/inward/record.url?scp=84979201720&partnerID=8YFLogxK

U2 - 10.1007/s00031-016-9401-x

DO - 10.1007/s00031-016-9401-x

M3 - Article

AN - SCOPUS:84979201720

SN - 1083-4362

VL - 22

SP - 885

EP - 910

JO - Transformation Groups

JF - Transformation Groups

IS - 4

ER -

B-ORBITS OF SQUARE ZERO IN NILRADICAL OF THE SYMPLECTIC ALGEBRA

Abstract

Bibliographical note

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this