Polynomials for GLp × GLq orbit closures in the flag variety

Benjamin J. Wyser; Alexander Yong

doi:10.1007/s00029-014-0152-z

Polynomials for GL_p × GL_q orbit closures in the flag variety

Benjamin J. Wyser, Alexander Yong

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

The subgroup K = GL_p× GL_q of GL_p+q acts on the (complex) flag variety 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.

Original language	English (US)
Pages (from-to)	1083-1110
Number of pages	28
Journal	Selecta Mathematica, New Series
Volume	20
Issue number	4
DOIs	https://doi.org/10.1007/s00029-014-0152-z
State	Published - Oct 2014

Keywords

Cohomology class representative
Flag variety
Kazhdan–Luztig–Vogan polynomials
Symmetric pair

ASJC Scopus subject areas

General Mathematics
General Physics and Astronomy

Online availability

10.1007/s00029-014-0152-z

Library availability

Discover UIUC Full Text

Cite this

@article{d6481403a07b44f0b72006e7c5416eeb,

title = "Polynomials for GLp × GLq orbit closures in the flag variety",

abstract = "The subgroup K = GLp× GLq of GLp+q acts on the (complex) flag variety GLp+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.",

keywords = "Cohomology class representative, Flag variety, Kazhdan–Luztig–Vogan polynomials, Symmetric pair",

author = "Wyser, {Benjamin J.} and Alexander Yong",

note = "Publisher Copyright: {\textcopyright} 2014, Springer Basel.",

year = "2014",

month = oct,

doi = "10.1007/s00029-014-0152-z",

language = "English (US)",

volume = "20",

pages = "1083--1110",

journal = "Selecta Mathematica, New Series",

issn = "1022-1824",

publisher = "Birkhauser Verlag Basel",

number = "4",

}

TY - JOUR

T1 - Polynomials for GLp × GLq orbit closures in the flag variety

AU - Wyser, Benjamin J.

AU - Yong, Alexander

PY - 2014/10

Y1 - 2014/10

N2 - The subgroup K = GLp× GLq of GLp+q acts on the (complex) flag variety GLp+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.

AB - The subgroup K = GLp× GLq of GLp+q acts on the (complex) flag variety GLp+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.

KW - Cohomology class representative

KW - Flag variety

KW - Kazhdan–Luztig–Vogan polynomials

KW - Symmetric pair

UR - http://www.scopus.com/inward/record.url?scp=84920157204&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84920157204&partnerID=8YFLogxK

U2 - 10.1007/s00029-014-0152-z

DO - 10.1007/s00029-014-0152-z

M3 - Article

AN - SCOPUS:84920157204

SN - 1022-1824

VL - 20

SP - 1083

EP - 1110

JO - Selecta Mathematica, New Series

JF - Selecta Mathematica, New Series

IS - 4

ER -