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

by Grant Walker & Reginald M. W. Wood
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eBook

Publisher: Cambridge University Press

Series: London Mathematical Society Lecture Note Series

Publication Date: October 31, 2017

ISBN: 9781108355926

Binding: Kobo eBook

Availability: eBook

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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.