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Polynomials and the mod 2 Steenrod Algebra: Volume 2, Representations of GL (n,F2)

Polynomials and the mod 2 Steenrod Algebra: Volume 2, Representations of GL (n,F2)
Author: Grant Walker
Publisher: Cambridge University Press
Total Pages: 382
Release: 2017-11-09
Genre: Mathematics
ISBN: 1108359280

Download Polynomials and the mod 2 Steenrod Algebra: Volume 2, Representations of GL (n,F2) Book in PDF, ePub and Kindle

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.


Polynomials and the mod 2 Steenrod Algebra

Polynomials and the mod 2 Steenrod Algebra
Author: Grant Walker
Publisher: Cambridge University Press
Total Pages: 381
Release: 2017-11-09
Genre: Mathematics
ISBN: 1108414451

Download Polynomials and the mod 2 Steenrod Algebra Book in PDF, ePub and Kindle

The second of two volumes covering the Steenrod algebra and its various applications. Ideal for researchers in pure mathematics.


Polynomials and the mod 2 Steenrod Algebra: Volume 2, Representations of GL (n,F2)

Polynomials and the mod 2 Steenrod Algebra: Volume 2, Representations of GL (n,F2)
Author: Grant Walker
Publisher: Cambridge University Press
Total Pages: 0
Release: 2017-11-09
Genre: Mathematics
ISBN: 9781108414456

Download Polynomials and the mod 2 Steenrod Algebra: Volume 2, Representations of GL (n,F2) Book in PDF, ePub and Kindle

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.


Polynomials and the mod 2 Steenrod Algebra: Volume 1, The Peterson Hit Problem

Polynomials and the mod 2 Steenrod Algebra: Volume 1, The Peterson Hit Problem
Author: Grant Walker
Publisher: Cambridge University Press
Total Pages: 372
Release: 2017-11-09
Genre: Mathematics
ISBN: 1108359299

Download Polynomials and the mod 2 Steenrod Algebra: Volume 1, The Peterson Hit Problem Book in PDF, ePub and Kindle

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.


Polynomials and the Mod 2 Steenrod Algebra

Polynomials and the Mod 2 Steenrod Algebra
Author: Grant Walker
Publisher: London Mathematical Society Le
Total Pages: 0
Release: 2018
Genre: Mathematics
ISBN: 9781108414067

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


Polynomial Representations of GLn

Polynomial Representations of GLn
Author: James Alexander Green
Publisher:
Total Pages: 132
Release: 1980
Genre: Electronic books
ISBN:

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The first half of this book contains the text of the first edition of LNM volume 830, Polynomial Representations of GLn. This classic account of matrix representations, the Schur algebra, the modular representations of GLn, and connections with symmetric groups, has been the basis of much research in representation theory. The second half is an Appendix, and can be read independently of the first. It is an account of the Littelmann path model for the case gln. In this case, Littelmann's 'paths' become 'words', and so the Appendix works with the combinatorics on words. This leads to the repesentation theory of the 'Littelmann algebra', which is a close analogue of the Schur algebra. The treatment is self- contained; in particular complete proofs are given of classical theorems of Schensted and Knuth.


Lectures on K(X).

Lectures on K(X).
Author: Raoul Bott
Publisher:
Total Pages: 161
Release: 1967
Genre:
ISBN:

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Exotic Properties of Superfluid 3He

Exotic Properties of Superfluid 3He
Author: G. E. Volovik
Publisher: World Scientific
Total Pages: 236
Release: 1992
Genre: Science
ISBN: 9789810207052

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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.