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  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.
|Title of host publication||Lie Theory and Its Applications in Physics|
|Publisher||Springer New York LLC|
|Number of pages||13|
|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
|Name||Springer Proceedings in Mathematics and Statistics|
|Conference||Proceedings of the 11th International Workshop on Lie Theory and Its Applications in Physics, 2015|
|Period||15/06/15 → 21/06/15|
Bibliographical noteFunding 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.
© Springer Nature Singapore Pte Ltd. 2016.
ASJC Scopus subject areas
- Mathematics (all)