[PDF] Polynomials And The Mod 2 Steenrod Algebra Volume 2 Representations Of Gl Nf2 eBook

Author : Grant Walker (Mathematician)
Publisher : Cambridge University Press
Page : 381 pages
File Size : 37,74 MB
Release : 2018
Category : Polynomials
ISBN : 1108414451

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This is the first book to link the mod 2 Steenrod algebra, a classical object of study in algebraic topology, with modular representations of matrix groups over the field F of two elements. The link is provided through a detailed study of Peterson's 'hit problem' concerning the action of the Steenrod algebra on polynomials, which remains unsolved except in special cases. The topics range from decompositions of integers as sums of 'powers of 2 minus 1', to Hopf algebras and the Steinberg representation of GL(n,F). Volume 1 develops the structure of the Steenrod algebra from an algebraic viewpoint and can be used as a graduate-level textbook. Volume 2 broadens the discussion to include modular representations of matrix groups.

Author : Grant Walker
Publisher : Cambridge University Press
Page : 381 pages
File Size : 14,19 MB
Release : 2017-11-09
Category : Mathematics
ISBN : 1108355927

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This is the first book to link the mod 2 Steenrod algebra, a classical object of study in algebraic topology, with modular representations of matrix groups over the field F of two elements. The link is provided through a detailed study of Peterson's `hit problem' concerning the action of the Steenrod algebra on polynomials, which remains unsolved except in special cases. The topics range from decompositions of integers as sums of 'powers of 2 minus 1', to Hopf algebras and the Steinberg representation of GL(n, F). Volume 1 develops the structure of the Steenrod algebra from an algebraic viewpoint and can be used as a graduate-level textbook. Volume 2 broadens the discussion to include modular representations of matrix groups.

Author : Grant Walker
Publisher : Cambridge University Press
Page : 371 pages
File Size : 43,30 MB
Release : 2018
Category : Mathematics
ISBN : 1108414486

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The first of two volumes covering the Steenrod algebra and its various applications. Suitable as a graduate text.

Author : Grant Walker
Publisher : London Mathematical Society Le
Page : 0 pages
File Size : 26,59 MB
Release : 2018
Category : Mathematics
ISBN : 9781108414067

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Two volumes detailing Steenrod algebra and its applications, with background material. Ideal for researchers in pure mathematics.

Author : G. E. Volovik
Publisher : World Scientific
Page : 244 pages
File Size : 33,15 MB
Release : 1992
Category : Science
ISBN : 9789810207069

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This book discusses the unique properties of superfluid phases of 3He, the condensed matter with the outmost broken symmetry, which combine in a surprising way the properties of ordered magnets, liquid crystals and superfluids. The complicated vacuum state of these phases with a large number of fermionic and bosonic quasiparticles and topological objects remains the vacuum in modern quantum field theories. Some of the objects and physical phenomena in 3He have strong analogy with the neutrino, W-bosons, weak interactions, gravity, chiral anomaly, Quantum Hall Effect and fractional statistics. As an example of topological objects, the quantized vortices in 3He phases are discussed in detail, including singular and continuous vortices, half-quantum vortices, broken symmetry in the vortex core and phase transitions between the vortex states with different symmetry and topology.

Author : Yuji Tachikawa
Publisher : Springer
Page : 236 pages
File Size : 32,57 MB
Release : 2014-10-15
Category : Science
ISBN : 331908822X

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Understanding the dynamics of gauge theories is crucial, given the fact that all known interactions are based on the principle of local gauge symmetry. Beyond the perturbative regime, however, this is a notoriously difficult problem. Requiring invariance under supersymmetry turns out to be a suitable tool for analyzing supersymmetric gauge theories over a larger region of the space of parameters. Supersymmetric quantum field theories in four dimensions with extended N=2 supersymmetry are further constrained and have therefore been a fertile field of research in theoretical physics for quite some time. Moreover, there are far-reaching mathematical ramifications that have led to a successful dialogue with differential and algebraic geometry. These lecture notes aim to introduce students of modern theoretical physics to the fascinating developments in the understanding of N=2 supersymmetric gauge theories in a coherent fashion. Starting with a gentle introduction to electric-magnetic duality, the author guides readers through the key milestones in the field, which include the work of Seiberg and Witten, Nekrasov, Gaiotto and many others. As an advanced graduate level text, it assumes that readers have a working knowledge of supersymmetry including the formalism of superfields, as well as of quantum field theory techniques such as regularization, renormalization and anomalies. After his graduation from the University of Tokyo, Yuji Tachikawa worked at the Institute for Advanced Study, Princeton and the Kavli Institute for Physics and Mathematics of the Universe. Presently at the Department of Physics, University of Tokyo, Tachikawa is the author of several important papers in supersymmetric quantum field theories and string theory.

Author : Armand Borel
Publisher : American Mathematical Soc.
Page : 394 pages
File Size : 17,40 MB
Release : 1979-06-30
Category : Mathematics
ISBN : 0821814370

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Part 2 contains sections on Automorphic representations and $L$-functions, Arithmetical algebraic geometry and $L$-functions