Representations of Elementary Abelian P-groups and Vector Bundles
Author : David J. Benson
Publisher :
Page : pages
File Size : 42,81 MB
Release : 2017
Category : MATHEMATICS
ISBN : 9781316809303
Author : David J. Benson
Publisher :
Page : pages
File Size : 42,81 MB
Release : 2017
Category : MATHEMATICS
ISBN : 9781316809303
Author : Eng-chye Tan
Publisher : World Scientific
Page : 426 pages
File Size : 44,75 MB
Release : 2004
Category : Mathematics
ISBN : 9812562508
This invaluable volume collects the expanded lecture notes of thosetutorials. The topics covered include uncertainty principles forlocally compact abelian groups, fundamentals of representations of"p"-adic groups, the Harish?Chandra?Howe local characterexpansion, classification of the square-integrable representationsmodulo cuspidal data, Dirac cohomology and Vogan's conjecture, multiplicity-free actions and Schur?Weyl?Howe duality.
Author : David J. Benson
Publisher : Cambridge University Press
Page : 347 pages
File Size : 16,5 MB
Release : 2017
Category : Mathematics
ISBN : 1107174171
An up to date study of recent progress in vector bundle methods in the representation theory of elementary abelian groups.
Author : Christopher M. Parsons
Publisher :
Page : pages
File Size : 46,43 MB
Release : 2018
Category :
ISBN :
Author : David Arnold
Publisher : Springer Science & Business Media
Page : 264 pages
File Size : 16,86 MB
Release : 2000-06-16
Category : Mathematics
ISBN : 9780387989822
The theme of this book is an exposition of connections between representations of finite partially ordered sets and abelian groups. Emphasis is placed throughout on classification, a description of the objects up to isomorphism, and computation of representation type, a measure of when classification is feasible. David M. Arnold is the Ralph and Jean Storm Professor of Mathematics at Baylor University. He is the author of "Finite Rank Torsion Free Abelian Groups and Rings" published in the Springer-Verlag Lecture Notes in Mathematics series, a co-editor for two volumes of conference proceedings, and the author of numerous articles in mathematical research journals.
Author : Czes Kosniowski
Publisher : Pitman Publishing
Page : 252 pages
File Size : 41,81 MB
Release : 1978
Category : Mathematics
ISBN :
Author : László Fuchs
Publisher :
Page : 154 pages
File Size : 17,23 MB
Release : 1980
Category : Abelian groups
ISBN :
Author : Tammo tom Dieck
Publisher :
Page : 30 pages
File Size : 41,3 MB
Release : 1969
Category : Abelian groups
ISBN :
Author : Thomas Ludsteck
Publisher :
Page : 164 pages
File Size : 30,86 MB
Release : 2008
Category :
ISBN :
Author : Nathan Mark Grieve
Publisher :
Page : 242 pages
File Size : 38,50 MB
Release : 2013
Category :
ISBN :
This thesis is comprised of three logically independent parts. As the title suggests, each part is related to vector bundles on abelian varieties. We first use Brill-Noether theory to study the geometry of a general curve in its canonical embedding. We prove that there is no $g$ for which the canonical embedding of a general curve of genus $g$ lies on the Segre embedding of any product of three or more projective spaces. We then consider non-degenerate line bundles on abelian varieties. Central to our work is Mumford's index theorem. We give an interpretation of this theorem, and then prove that non-degenerate line bundles, with nonzero index, exhibit positivity analogous to ample line bundles. As an application, we determine the asymptotic behaviour of families of cup-product maps. Using this result, we prove that vector bundles, which are associated to these families, are asymptotically globally generated. To illustrate our results, we consider explicit examples. We also prove that simple abelian varieties, for which our results apply in all possible instances, exist. This is achieved by considering a particular class of abelian varieties with real multiplication. The final part of this thesis concerns the theory of theta and adelic theta groups. We extend and refine work of Mumford, Umemura, and Mukai. For example, we determine the structure and representation theory of theta groups associated to a class of vector bundles which we call simple semi-homogeneous vector bundles of separable type. We also construct, and clarify functorial properties enjoyed by, adelic theta groups associated to line bundles.