On the structure of Borel stable abelian subalgebras in infinitesimal symmetric spaces

Marco Pasquali; Paola Cellini; Paolo Papi; Pierluigi Moseneder Frajria

arxiv: 1109.4501 · v2 · pith:G44X3PVEnew · submitted 2011-09-21 · 🧮 math.RT · math.CO

On the structure of Borel stable abelian subalgebras in infinitesimal symmetric spaces

Paola Cellini , Pierluigi Moseneder Frajria , Paolo Papi , Marco Pasquali This is my paper

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keywords abelianborelstablesubalgebrasalgebracasesdimensionelements

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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.

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On the structure of Borel stable abelian subalgebras in infinitesimal symmetric spaces

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