Polynomials for \mathrm{GL}_p\times \mathrm{GL}_q orbit closures in the flag variety |
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Authors: | Benjamin J Wyser Alexander Yong |
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Institution: | 1. Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, IL, 61801, USA
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Abstract: | The subgroup \(K=\mathrm{GL}_p \times \mathrm{GL}_q\) of \(\mathrm{GL}_{p+q}\) acts on the (complex) flag variety \(\mathrm{GL}_{p+q}/B\) with finitely many orbits. We introduce a family of polynomials specializing representatives for cohomology classes of the orbit closures in the Borel model. We define and study \(K\) -orbit determinantal ideals to support the geometric naturality of these representatives. Using a modification of these ideals, we describe an analogy between two local singularity measures: the \(H\) -polynomials and the Kazhdan–Lusztig–Vogan polynomials. |
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