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Gelfand-Zetlin Polytopes and the Geometry of Flag Varieties

Villella, Elise (2019) Gelfand-Zetlin Polytopes and the Geometry of Flag Varieties. Doctoral Dissertation, University of Pittsburgh. (Unpublished)

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Gelfand-Zetlin polytopes are important in the finite dimensional representation theory of SLn(C) and the symplectic geometry of coadjoint orbits of the unitary group. We examine the combinatorics of Gelfand-Zetlin polytopes in relation to the geometry of the flag variety of SLn(C). The two main contributions of the thesis are as follows: (1) we describe virtual Gelfand-Zetlin polytopes associated to non-dominant weights and (2) we identify the cohomology ring of the flag variety with a quotient of the subalgebra of the Chow cohomology ring of the Gelfand-Zetlin toric variety generated in degree one. More precisely, we take the largest quotient of this subalgebra that satisfies Poincare duality.


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Item Type: University of Pittsburgh ETD
Status: Unpublished
CreatorsEmailPitt UsernameORCID
Villella, Eliseemv23@pitt.eduemv23
ETD Committee:
TitleMemberEmail AddressPitt UsernameORCID
Committee ChairKaveh, Kiumarskaveh@pitt.edukaveh
Committee MemberHarada,
Committee MemberIon, Bogdanbion@pitt.edubion
Committee MemberDeBlois, Jasonjdeblois@pitt.edujdeblois
Date: 26 September 2019
Date Type: Publication
Defense Date: 7 August 2019
Approval Date: 26 September 2019
Submission Date: 24 June 2019
Access Restriction: No restriction; Release the ETD for access worldwide immediately.
Number of Pages: 79
Institution: University of Pittsburgh
Schools and Programs: Dietrich School of Arts and Sciences > Mathematics
Degree: PhD - Doctor of Philosophy
Thesis Type: Doctoral Dissertation
Refereed: Yes
Uncontrolled Keywords: algebraic geometry
Date Deposited: 26 Sep 2019 13:10
Last Modified: 26 Sep 2019 13:10

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