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

by Grant Walker, Reginald M. W. Wood

Overview

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.

Product Details

ISBN-13:	9781108414456
Publisher:	Cambridge University Press
Publication date:	11/09/2017
Series:	London Mathematical Society Lecture Note Series , #442
Pages:	378
Product dimensions:	5.98(w) x 8.94(h) x 0.91(d)

About the Author

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.

Table of Contents

Preface; 16. The action of GL(n) on flags; 17. Irreducible F2GL(n)-modules; 18. Idempotents and characters; 19. Splitting P(n) as an A2-module; 20. The algebraic group Ḡ(n); 21. Endomorphisms of P(n) over A2; 22. The Steinberg summands of P(n); 23. The d-spike module J(n); 24. Partial flags and J(n); 25. The symmetric hit problem; 26. The dual of the symmetric hit problem; 27. The cyclic splitting of P(n); 28. The cyclic splitting of DP(n); 29. The 4-variable hit problem, I; 30. The 4-variable hit problem, II; Bibliography; Index of Notation for Volume 2; Index for Volume 2; Index of Notation for Volume 1; Index for Volume 1.

Editorial Reviews

'In these volumes, the authors draw upon the work of many researchers in addition to their own work, in places presenting new proofs or improvements of results. Moreover, the material in Volume 2 using the cyclic splitting of P(n) is based in part upon the unpublished Ph.D. thesis of Helen Weaver … Much of the material covered has not hitherto appeared in book form, and these volumes should serve as a useful reference. … readers will find different aspects appealing.' Geoffrey M. L. Powell, Mathematical Reviews

From the Publisher