Abstract
We give an explicit description of the closure containment order (or “Bruhat order”) on the set of orbits of \(GL_p \times GL_q\) on the flag variety \(GL_{p+q}/B\), relative to the parametrization of the orbits by combinatorial objects called “clans”. This leads to a corresponding description of the closures of such orbits as sets of flags satisfying certain incidence conditions encoded by the parametrizing clans.
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The author was supported by NSF International Research Fellowship 1159045 and hosted by Institut Fourier in Grenoble, France.
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Wyser, B.J. The Bruhat order on clans. J Algebr Comb 44, 495–517 (2016). https://doi.org/10.1007/s10801-016-0678-6
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DOI: https://doi.org/10.1007/s10801-016-0678-6