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Motivated by relating the representation theory of the split real and p-adic forms of a connected reductive algebraic group G, we describe a subset of \(2^r\) orbits on the complex flag variety for a certain symmetric subgroup. (Here r is the semisimple rank of G.) This set of orbits has the property that, while the closure of individual orbits are generally singular, they are always smooth along other orbits in the set. This, in turn, implies consequences for the representation theory of the split real group.

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A Note on the Orbits of a Symmetric Subgroup in the Flag Variety

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  • 发表日期：

    2025年

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  • Leticia Barchini,
  • Peter E. Trapa

摘要

Motivated by relating the representation theory of the split real and p-adic forms of a connected reductive algebraic group G, we describe a subset of \(2^r\) orbits on the complex flag variety for a certain symmetric subgroup. (Here r is the semisimple rank of G.) This set of orbits has the property that, while the closure of individual orbits are generally singular, they are always smooth along other orbits in the set. This, in turn, implies consequences for the representation theory of the split real group.