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

N1 - Funding Information: We would like to thank Dmitri Panyushev for sharing his paper with us and for discussions during this work. N. Barnea was partially supported by Israel Scientific Foundation grant 797/14. Publisher Copyright: © Springer Nature Singapore Pte Ltd. 2016.

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 - http://www.scopus.com/inward/record.url?scp=85009784183&partnerID=8YFLogxK

U2 - https://doi.org/10.1007/978-981-10-2636-2_28

DO - https://doi.org/10.1007/978-981-10-2636-2_28

M3 - Conference contribution

SN - 9789811026355

T3 - Springer Proceedings in Mathematics and Statistics

SP - 399

EP - 411

BT - Lie Theory and Its Applications in Physics

A2 - Dobrev, Vladimir

Y2 - 15 June 2015 through 21 June 2015

ER -