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Polynomials and the mod 2 Steenrod Algebra

Author: Grant Walker, (Mathematician); Reginald M W Wood
Publisher: Cambridge, United Kingdom ; New York, NY, USA : Cambridge University Press, 2018.
Series: London Mathematical Society lecture note series, 441-442.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:
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  Read more...
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Additional Physical Format: Online version, v.1:
Walker, Grant, 1960-
Polynomials and the mod 2 Steenrod Algebra : Volume 1: The Peterson Hit Problem.
Cambridge Cambridge University Press 2018
(OCoLC)1013722827
Online version, v.2:
Walker, Grant, 1960-
Polynomials and the mod 2 Steenrod algebra. volume 2, representations of GL(n,F₂).
Cambridge : Cambridge University Press, 2018
(OCoLC)1013737213
Document Type: Book
All Authors / Contributors: Grant Walker, (Mathematician); Reginald M W Wood
ISBN: 9781108414067 1108414060 9781108414487 1108414486 9781108414456 1108414451
OCLC Number: 1015730861
Description: 2 volumes (xxiv, 346 pages; xxiv, 355 pages) : illustrations ; 23 cm.
Contents: v. 1. The Peterson hit problem. Steenrod squares and the hit problem ; Conjugate Steenrod squares ; The Steenrod algebra A2 ; Products and conjugation in A2 ; Combinatorial structures ; The cohit module Q(n) ; Bounds for dimQd(n) ; Special blocks and a basis for Q(3) ; The dual of the hit problem ; K(3) and Q(3) as F2GL(3)-modules ; The dual of the Steenrod algebra ; Further structure of A2 ; Stripping and nilpotence in A2 ; The 2-dominance theorem ; Invariants and the hit problem --
v. 2. Representations of GL(n,F₂). The action of GL(n) on flags ; Irreducible F2GL(n)-modules ; Idempotents and characters ; Splitting P(n) as an A2-module ; The algebraic group G(n) ; Endomorphisms of P(n) over A2 ; The Steinberg summands of P(n) ; The d-spike module J(n) ; Partial flags and J(n) ; The symmetric hit problem ; The dual of the symmetric hit problem ; The cyclic splitting of P(n) ; The cyclic splitting of DP(n) ; The 4-variable hit problem, I ; The 4-variable hit problem, II.
Series Title: London Mathematical Society lecture note series, 441-442.
Responsibility: Grant Walker, University of Manchester, Reginald M. W. Wood, University of Manchester.

Abstract:

This detailed two-volume reference on the Steenrod algebra and its various applications presents more than thirty years of research. Developing the structure of the Steenrod algebra from an algebraic  Read more...

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'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 Read more...

 
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