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.
General
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