Grant Walker,
Reginald M. W. Wood
Cambridge University Press
e druk, 2017
9781108414456
Polynomials and the mod 2 Steenrod Algebra: Volume 2, Representations of GL (n,F2)
Specificaties
Paperback, 378 blz.
|
Engels
Cambridge University Press |
e druk, 2017
ISBN13: 9781108414456
Rubricering
Onderdeel van serie
London Mathematical
Levertijd ongeveer 8 werkdagen
Samenvatting
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.
Specificaties
ISBN13:9781108414456
Taal:Engels
Bindwijze:Paperback
Aantal pagina's:378
Uitgever:Cambridge University Press
Serie:London Mathematical
Inhoudsopgave
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.