Polynomials and the mod 2 Steenrod Algebra

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.