B-orbits in abelian nilradicals of types B, C and D: towards a conjecture of Panyushev

2016/01/12 by Nurit Barnea, Barnea, Nurit, Anna Melnikov +1
Mathematics · #FOS: Mathematics #Representation Theory (math.RT) #math.RT

paper · pdf · doi:10.48550/arxiv.1601.02731

12 pages

arxiv created 2016/01/12 · arxiv updated 2016/01/13

Abstract

Let B be a Borel subgroup of a semisimple algebraic group G and let \mathfrak m be an abelian nilradical in \mathfrak b=\rm Lie (B). Using subsets of strongly orthogonal roots in the subset of positive roots corresponding to \mathfrak m, D. Panyushev \citePan gives in particular classification of B-orbits in \mathfrak m and \mathfrak m^* and states general conjectures on the closure and dimensions of the B-orbits in both \mathfrak m and \mathfrak m^* in terms of involutions of the Weyl group. Using Pyasetskii correspondence between B-orbits in \mathfrak m and \mathfrak 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.

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