Polynomials and the mod 2 Steenrod Algebra: Volume 2, Representations of GL (n,F2) London Mathematical Society Lecture Note Series
Langue : Anglais
Auteurs : Walker Grant, Wood Reginald M. W.
The second of two volumes covering the Steenrod algebra and its various applications. Ideal for researchers in pure mathematics.
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.
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.
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.
Reginald M. W. Wood was a Professor in the School of Mathematics at the University of Manchester before his retirement in 2005.
Date de parution : 11-2017
Ouvrage de 378 p.
15.2x22.7 cm
Thème de Polynomials and the mod 2 Steenrod Algebra: Volume 2... :
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