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

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Grant Walker (University of Manchester) Reginald M. W. Wood (University of Manchester)

Polynomials and the mod 2 Steenrod Algebra

Volume 2, Representations of GL (n,F2)

Grant Walker (University of Manchester), Reginald M. W. Wood (University of Manchester)

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English

Cambridge University Press
09 November 2017

Algebra; Topology

Series: London Mathematical Society Lecture Note Series

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.

By: Grant Walker (University of Manchester), Reginald M. W. Wood (University of Manchester)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Volume: 442
Dimensions: Height: 227mm, Width: 152mm, Spine: 23mm
Weight: 550g
ISBN: 9781108414456
ISBN 10: 1108414451
Series: London Mathematical Society Lecture Note Series
Pages: 378
Publication Date: 09 November 2017
Audience: Professional and scholarly , College/higher education , Undergraduate , Further / Higher Education
Format: Paperback
Publisher's Status: Active

Preface; 16. The action of GL(n) on flags; 17. Irreducible F2GL(n)-modules; 18. Idempotents and characters; 19. Splitting P(n) as an A2-module; 20. The algebraic group Ḡ(n); 21. Endomorphisms of P(n) over A2; 22. The Steinberg summands of P(n); 23. The d-spike module J(n); 24. Partial flags and J(n); 25. The symmetric hit problem; 26. The dual of the symmetric hit problem; 27. The cyclic splitting of P(n); 28. The cyclic splitting of DP(n); 29. The 4-variable hit problem, I; 30. The 4-variable hit problem, II; Bibliography; Index of Notation for Volume 2; Index for Volume 2; Index of Notation for Volume 1; Index for Volume 1.

Grant Walker was a senior lecturer in the School of Mathematics at the University of Manchester before his retirement in 2005. Reginald M. W. Wood was a Professor in the School of Mathematics at the University of Manchester before his retirement in 2005.

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

'In these volumes, the authors draw upon the work of many researchers in addition to their own work, in places presenting new proofs or improvements of results. Moreover, the material in Volume 2 using the cyclic splitting of P(n) is based in part upon the unpublished Ph.D. thesis of Helen Weaver ... Much of the material covered has not hitherto appeared in book form, and these volumes should serve as a useful reference. ... readers will find different aspects appealing.' Geoffrey M. L. Powell, Mathematical Reviews 'In these volumes, the authors draw upon the work of many researchers in addition to their own work, in places presenting new proofs or improvements of results. Moreover, the material in Volume 2 using the cyclic splitting of P(n) is based in part upon the unpublished Ph.D. thesis of Helen Weaver ... Much of the material covered has not hitherto appeared in book form, and these volumes should serve as a useful reference. ... readers will find different aspects appealing.' Geoffrey M. L. Powell, Mathematical Reviews