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Degeneracy loci and G2 flags.

University of Michigan.

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Degeneracy loci and G2 flags.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Degeneracy loci and G2 flags./
Author:	Anderson, David E.
Description:	128 p.
Notes:	Adviser: William Fulton.
Contained By:	Dissertation Abstracts International70-04B.
Subject:	Mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3354004
ISBN:	9781109110746

Degeneracy loci and G2 flags.
Anderson, David E.

Degeneracy loci and G2 flags. - 128 p.

Adviser: William Fulton.

Thesis (Ph.D.)--University of Michigan, 2009.

As part of our description of the G2 flag variety, we prove some basic facts about octonions and trilinear forms, and give a natural construction of octonion algebra bundles which appears to be new.

ISBN: 9781109110746Subjects--Topical Terms:

515831
Mathematics.

Degeneracy loci and G2 flags.
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020 $a 9781109110746
035 $a (UMI)AAI3354004
035 $a AAI3354004
040 $a UMI $c UMI
100 1 $a Anderson, David E. $3 1032087
245 1 0 $a Degeneracy loci and G2 flags.
300 $a 128 p.
500 $a Adviser: William Fulton.
500 $a Source: Dissertation Abstracts International, Volume: 70-04, Section: B, page: 2332.
502 $a Thesis (Ph.D.)--University of Michigan, 2009.
520 $a As part of our description of the G2 flag variety, we prove some basic facts about octonions and trilinear forms, and give a natural construction of octonion algebra bundles which appears to be new.
520 $a We define degeneracy loci for vector bundles with structure group G2, and give formulas for their cohomology (or Chow) classes in terms of the Chern classes of the bundles involved. When the base is a point, such formulas are part of the theory for projective homogeneous spaces developed by Bernstein-Gelfand-Gelfand and Demazure. This has been extended to the setting of general algebraic geometry by Giambelli-Thom-Porteous, Kempf-Laksov, and Fulton in classical types; the present work carries out the analogous program in type G2. We include explicit descriptions of the G2 flag variety and its Schubert varieties, and several computations, including one that answers a question of William Graham.
520 $a Motivated by the relationship between symmetric matrices and the symplectic group, we define a new type of symmetry for morphisms of vector bundles, called triality symmetry. We explain the relation with G2, and deduce degeneracy locus formulas for triality-symmetric morphisms from formulas for Schubert loci in G2 flag bundles. We also give a proof of the formulas in terms of equivariant cohomology, by computing the classes of P-orbits in g2/p for a parabolic subgroup P ⊂ G 2.
520 $a In five appendices, we collect some facts from representation theory; review the phenomenon of triality and its relation to G 2 flags; discuss a general notion of symmetry for morphisms of vector bundles; give parametrizations of Schubert cells, formulas for degeneracy loci, and the equivariant multiplication table for the G 2 flag variety; and compute the Chow rings of quadric bundles.
590 $a School code: 0127.
650 4 $a Mathematics. $3 515831
690 $a 0405
710 2 $a University of Michigan. $3 777416
773 0 $t Dissertation Abstracts International $g 70-04B.
790 $a 0127
790 1 0 $a Fulton, William, $e advisor
791 $a Ph.D.
792 $a 2009
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3354004