B–Orbits in Abelian Nilradicals of types B,C and D: Towards a conjecture of Panyushev

Nurit Barnea; Anna Melnikov

doi:10.1007/978-981-10-2636-2_28

B–Orbits in Abelian Nilradicals of types B,C and D: Towards a conjecture of Panyushev

Nurit Barnea
, Anna Melnikov

Department of Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

Let B be a Borel subgroup of a semisimple algebraic group G and let m be an abelian nilradical in b = Lie(B). Using subsets of strongly orthogonal roots in the subset of positive roots corresponding to m, D. Panyushev [1] gives in particular classification of B−orbits in m and m* and states general conjectures on the closure and dimensions of the B−orbits in both m and m* in terms of involutions of the Weyl group. Using Pyasetskii correspondence between B−orbits in m and m* he shows the equivalence of these two conjectures. In this Note we prove his conjecture in types B_n,C_n and D_n for adjoint case.

Original language	English
Title of host publication	Lie Theory and Its Applications in Physics
Editors	Vladimir Dobrev
Publisher	Springer New York LLC
Pages	399-411
Number of pages	13
ISBN (Print)	9789811026355
DOIs	https://doi.org/10.1007/978-981-10-2636-2_28
State	Published - 2016
Event	Proceedings of the 11th International Workshop on Lie Theory and Its Applications in Physics, 2015 - Varna, Bulgaria Duration: 15 Jun 2015 → 21 Jun 2015

Publication series

Name	Springer Proceedings in Mathematics and Statistics
Volume	191
ISSN (Print)	2194-1009
ISSN (Electronic)	2194-1017

Conference

Conference	Proceedings of the 11th International Workshop on Lie Theory and Its Applications in Physics, 2015
Country/Territory	Bulgaria
City	Varna
Period	15/06/15 → 21/06/15

Bibliographical note

Publisher Copyright:
© Springer Nature Singapore Pte Ltd. 2016.

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1007/978-981-10-2636-2_28

Cite this

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title = "B–Orbits in Abelian Nilradicals of types B,C and D: Towards a conjecture of Panyushev",

abstract = "Let B be a Borel subgroup of a semisimple algebraic group G and let m be an abelian nilradical in b = Lie(B). Using subsets of strongly orthogonal roots in the subset of positive roots corresponding to m, D. Panyushev [1] gives in particular classification of B−orbits in m and m* and states general conjectures on the closure and dimensions of the B−orbits in both m and m* in terms of involutions of the Weyl group. Using Pyasetskii correspondence between B−orbits in m and m* he shows the equivalence of these two conjectures. In this Note we prove his conjecture in types Bn,Cn and Dn for adjoint case.",

author = "Nurit Barnea and Anna Melnikov",

note = "Publisher Copyright: {\textcopyright} Springer Nature Singapore Pte Ltd. 2016.; Proceedings of the 11th International Workshop on Lie Theory and Its Applications in Physics, 2015 ; Conference date: 15-06-2015 Through 21-06-2015",

year = "2016",

doi = "10.1007/978-981-10-2636-2\_28",

language = "English",

isbn = "9789811026355",

series = "Springer Proceedings in Mathematics and Statistics",

publisher = "Springer New York LLC",

pages = "399--411",

editor = "Vladimir Dobrev",

booktitle = "Lie Theory and Its Applications in Physics",

}

Barnea, N & Melnikov, A 2016, B–Orbits in Abelian Nilradicals of types B,C and D: Towards a conjecture of Panyushev. in V Dobrev (ed.), Lie Theory and Its Applications in Physics. Springer Proceedings in Mathematics and Statistics, vol. 191, Springer New York LLC, pp. 399-411, Proceedings of the 11th International Workshop on Lie Theory and Its Applications in Physics, 2015, Varna, Bulgaria, 15/06/15. https://doi.org/10.1007/978-981-10-2636-2_28

B–Orbits in Abelian Nilradicals of types B,C and D: Towards a conjecture of Panyushev. / Barnea, Nurit; Melnikov, Anna.
Lie Theory and Its Applications in Physics. ed. / Vladimir Dobrev. Springer New York LLC, 2016. p. 399-411 (Springer Proceedings in Mathematics and Statistics; Vol. 191).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - B–Orbits in Abelian Nilradicals of types B,C and D

T2 - Proceedings of the 11th International Workshop on Lie Theory and Its Applications in Physics, 2015

AU - Barnea, Nurit

AU - Melnikov, Anna

PY - 2016

Y1 - 2016

N2 - Let B be a Borel subgroup of a semisimple algebraic group G and let m be an abelian nilradical in b = Lie(B). Using subsets of strongly orthogonal roots in the subset of positive roots corresponding to m, D. Panyushev [1] gives in particular classification of B−orbits in m and m* and states general conjectures on the closure and dimensions of the B−orbits in both m and m* in terms of involutions of the Weyl group. Using Pyasetskii correspondence between B−orbits in m and m* he shows the equivalence of these two conjectures. In this Note we prove his conjecture in types Bn,Cn and Dn for adjoint case.

AB - Let B be a Borel subgroup of a semisimple algebraic group G and let m be an abelian nilradical in b = Lie(B). Using subsets of strongly orthogonal roots in the subset of positive roots corresponding to m, D. Panyushev [1] gives in particular classification of B−orbits in m and m* and states general conjectures on the closure and dimensions of the B−orbits in both m and m* in terms of involutions of the Weyl group. Using Pyasetskii correspondence between B−orbits in m and m* he shows the equivalence of these two conjectures. In this Note we prove his conjecture in types Bn,Cn and Dn for adjoint case.

UR - https://www.scopus.com/pages/publications/85009784183

U2 - 10.1007/978-981-10-2636-2_28

DO - 10.1007/978-981-10-2636-2_28

M3 - Conference contribution

AN - SCOPUS:85009784183

SN - 9789811026355

T3 - Springer Proceedings in Mathematics and Statistics

SP - 399

EP - 411

BT - Lie Theory and Its Applications in Physics

A2 - Dobrev, Vladimir

PB - Springer New York LLC

Y2 - 15 June 2015 through 21 June 2015

ER -

B–Orbits in Abelian Nilradicals of types B,C and D: Towards a conjecture of Panyushev

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