Cotangent Schubert Calculus in Grassmannians

We find formulas for the Segre-MacPherson classes of Schubert cells in T-equivariant cohomology and the motivic Segre classes of Schubert cells in T-equivariant K-theory. In doing so we look at the pushforward of the projection map from the Bott-Samelson (Kempf-Laksov) desingularization to the Grassmannian. We find that the Segre-MacPherson classes are stable under pullbacks of maps embedding a Grassmannian into a bigger Grassmannian. We also express these formulas using certain Demazure-Lusztig operators that have previously been used to study these classes.

Name thesis:degree_name

Doctor of Philosophy

Level thesis:degree_level

doctoral

Discipline thesis:degree_discipline

Mathematics

Department dc:contributor.department

Mathematics

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

2022

Author dc:creator

• Oetjen, David Christopher

Chair dc:contributor.committeechair

• Mihalcea, Constantin Leonardo

Committee members dc:contributor.committeemember

• Shimozono, Mark M.
• Haskell, Peter E.
• Orr, Daniel D.

• Equivariant Cohomology
• Equivariant K-Theory
• Bott-Samelson Variety
• Segre-MacPherson Class
• Motivic Segre Class
• Demazure-Lusztig Operator

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Language dc:language.iso

en

Dc Identifier Other

vt_gsexam:35013

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/110798