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

Grant Walker · Reginald M. W. Wood

nov 2017 · London Mathematical Society Lecture Note Series Libro 442 · Cambridge University Press

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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.

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Grant Walker was a senior lecturer in the School of Mathematics at the University of Manchester before his retirement in 2005.

Reginald M. W. Wood was a Professor in the School of Mathematics at the University of Manchester before his retirement in 2005.