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arXiv · 1705.03117

Polarized relations on horizontal SL(2)s

Matt Kerr·Gregory Pearlstein·Colleen Robles
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Abstract

We introduce a relation on real conjugacy classes of SL(2)-orbits in a Mumford-Tate domain D which is compatible with natural partial orders on the sets of nilpotent orbits in the corresponding Lie algebra and boundary orbits in the compact dual. A generalization of the SL(2)-orbit theorem to such domains leads to an algorithm for computing this relation, which is worked out in several examples and special cases including period domains, Hermitian symmetric domains, and complete flag domains, and used to define a poset of equivalence classes of multivariable nilpotent orbits on D.

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Matt Kerr, Gregory Pearlstein, Colleen Robles. 2017-05-08. Polarized relations on horizontal SL(2)s. https://arxiv.org/abs/1705.03117

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