London Mathematical Society Lecture Note Ser.: Polynomials and the Mod 2 ...
Polynomials and the mod 2 Steenrod Algebra: Volume 2, Representations of GL (n,F2)Author(s): Grant Walker, Reginald M. W. Wood\nFormat: Paperback\nPublisher: Cambridge University Press, United Kingdom\nImprint: Cambridge University Press\nISBN-13: 9781108414456, 978-1108414456\nSynopsis\nThis 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 represe.
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