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Structure of Quiver Polynomials and ...

Kaliszewski, Ryan.

Structure of Quiver Polynomials and Schur Positivity.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Structure of Quiver Polynomials and Schur Positivity.
Author:	Kaliszewski, Ryan.
Description:	66 p.
Notes:	Source: Dissertation Abstracts International, Volume: 74-09(E), Section: B.
Notes:	Adviser: Richard Rimanyi.
Contained By:	Dissertation Abstracts International74-09B(E).
Subject:	Mathematics.
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3562917
ISBN:	9781303108105

Structure of Quiver Polynomials and Schur Positivity.
Kaliszewski, Ryan.

Structure of Quiver Polynomials and Schur Positivity. - 66 p.

Source: Dissertation Abstracts International, Volume: 74-09(E), Section: B.

Thesis (Ph.D.)--The University of North Carolina at Chapel Hill, 2013.

Given a directed graph (quiver) and an association of a natural number to each vertex, one can construct a representation of a Lie group on a vector space. If the underlying, undirected graph of the quiver is a Dynkin graph of A-, D-, or E-type then the action has finitely many orbits. The equivariant fundamental classes of the orbit closures are the key objects of study in this paper. These fundamental classes are polynomials in universal Chern classes of a classifying space so they are referred to as "quiver polynomials."

ISBN: 9781303108105Subjects--Topical Terms:

184409
Mathematics.

Structure of Quiver Polynomials and Schur Positivity.
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020 $a 9781303108105
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100 1 $a Kaliszewski, Ryan. $3 660294
245 1 0 $a Structure of Quiver Polynomials and Schur Positivity.
300 $a 66 p.
500 $a Source: Dissertation Abstracts International, Volume: 74-09(E), Section: B.
500 $a Adviser: Richard Rimanyi.
502 $a Thesis (Ph.D.)--The University of North Carolina at Chapel Hill, 2013.
520 $a Given a directed graph (quiver) and an association of a natural number to each vertex, one can construct a representation of a Lie group on a vector space. If the underlying, undirected graph of the quiver is a Dynkin graph of A-, D-, or E-type then the action has finitely many orbits. The equivariant fundamental classes of the orbit closures are the key objects of study in this paper. These fundamental classes are polynomials in universal Chern classes of a classifying space so they are referred to as "quiver polynomials."
520 $a It has been shown by A. Buch [B08] that these polynomials can be expressed in terms of Schur-type functions. Buch further conjectures that in this expression the coefficients are non-negative.
520 $a Our goal is to study the coefficients and structure of these quiver polynomials using an iterated residue description due to R. Rimanyi [RR]. We introduce the Jacobi-Trudi transform, which creates an equivalence realtion on rational functions, to show that Buch's conjecture holds for a quiver polynomial if and only if there is a representative in the equivalence class that is Schur positive. Also we define a notion of strong Schur positivity and demonstrate the connection between this and Schur positivity, proving Schur positivity for some special cases of quiver polynomials.
590 $a School code: 0153.
650 4 $a Mathematics. $3 184409
650 4 $a Applied Mathematics. $3 530992
690 $a 0405
690 $a 0364
710 2 $a The University of North Carolina at Chapel Hill. $b Mathematics. $3 660295
773 0 $t Dissertation Abstracts International $g 74-09B(E).
790 $a 0153
791 $a Ph.D.
792 $a 2013
793 $a English
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3562917

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