Polynomials and the mod 2 Steenrod Algebra

Erscheinungsjahr 2018
ISBN: 978-1-108-41445-6
Verlag: Cambridge University Press

Buch, Englisch, Band 442, 378 Seiten, Format (B × H): 152 mm x 229 mm, Gewicht: 549 g

Reihe: London Mathematical Society Lecture Note Series

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.

Autoren/Hrsg.

Walker, Grant

Wood, Reginald M. W.

Inhaltsverzeichnis

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 ?(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.

Über Autor(innen)

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

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