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
DOI: 10.1007/s00029-014-0152-z
Enlaces
- Texto completo
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.