Cohomology classes of conormal bundles of Schubert varieties and Yangian weight functions

If you need an accessible version of this item, please email your request to digschol@iu.edu so that they may create one and provide it to you.
Date
2014-08
Language
English
Embargo Lift Date
Committee Members
Degree
Degree Year
Department
Grantor
Journal Title
Journal ISSN
Volume Title
Found At
Springer
Abstract

We consider the conormal bundle of a Schubert variety SI in the cotangent bundle T∗Gr of the Grassmannian Gr of k-planes in Cn. This conormal bundle has a fundamental class κI in the equivariant cohomology H∗T(T∗Gr). Here T=(C∗)n×C∗. The torus (C∗)n acts on T∗Gr in the standard way and the last factor C∗ acts by multiplication on fibers of the bundle. We express this fundamental class as a sum YI of the Yangian Y(gl2) weight functions (WJ)J. We describe a relation of YI with the double Schur polynomial [SI]. A modified version of the κI classes, named κ′I, satisfy an orthogonality relation with respect to an inner product induced by integration on the non-compact manifold T∗Gr. This orthogonality is analogous to the well known orthogonality satisfied by the classes of Schubert varieties with respect to integration on Gr. The classes (κ′I)I form a basis in the suitably localized equivariant cohomology H∗T(T∗Gr). This basis depends on the choice of the coordinate flag in Cn. We show that the bases corresponding to different coordinate flags are related by the Yangian R-matrix.

Description
item.page.description.tableofcontents
item.page.relation.haspart
Cite As
Rimányi, R., Tarasov, V., & Varchenko, A. (2014). Cohomology classes of conormal bundles of Schubert varieties and Yangian weight functions. Mathematische Zeitschrift, 277(3–4), 1085–1104. https://doi.org/10.1007/s00209-014-1295-5
ISSN
Publisher
Series/Report
Sponsorship
Major
Extent
Identifier
Relation
Journal
Mathematische Zeitschrift
Source
ArXiv
Alternative Title
Type
Article
Number
Volume
Conference Dates
Conference Host
Conference Location
Conference Name
Conference Panel
Conference Secretariat Location
Version
Author's manuscript
Full Text Available at
This item is under embargo {{howLong}}