Polynomials for GLp×GLq orbit closures in the flag variety

• Benjamin J. Wyser ^[1] ; Alexander Yong ^[1]
  1. [1] University of Illinois at Urbana Champaign

     University of Illinois at Urbana Champaign

     Township of Cunningham, Estados Unidos

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 20, Nº. 4, 2014, págs. 1083-1110
• Idioma: inglés
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• Resumen

  • The subgroup K=GLp×GLqK=GLp×GLq of GLp+qGLp+q acts on the (complex) flag variety GLp+q/BGLp+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 KK -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 HH -polynomials and the Kazhdan–Lusztig–Vogan polynomials.