On the structure of Borel stable abelian subalgebras in infinitesimal symmetric spaces
arXiv:1109.4501 · doi:10.1007/s00029-012-0097-z
Abstract
Let g=g_0+g_1 be a Z_2-graded Lie algebra. We study the posets of abelian subalgebras of g_1 which are stable w.r.t. a Borel subalgebra of g_0. In particular, we find out a natural parametrization of maximal elements and dimension formulas for them. We recover as special cases several results of Kostant, Panyushev, Suter.
Latex file, 35 pages, minor corrections, some examples added. To appear in Selecta Mathematica