Polynomials and the mod 2 Steenrod Algebra
Volume 2. Representations of GL (n,F2)
$99.99 (C)
Part of London Mathematical Society Lecture Note Series
 Authors:
 Grant Walker, University of Manchester
 Reginald M. W. Wood, University of Manchester
 Date Published: January 2018
 availability: Available
 format: Paperback
 isbn: 9781108414456
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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 graduatelevel textbook. Volume 2 broadens the discussion to include modular representations of matrix groups.
Read more Algebraic and combinatorial treatment of Steenrod algebra
 Accessible to those without a background in topology
 Largely selfcontained with detailed proofs
Reviews & endorsements
'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 Moreover, the material in Volume 2 using the cyclic splitting of P(n) is based in part upon the unpublished Ph.D. thesis of Helen Weaver … Much of the material covered has not hitherto appeared in book form, and these volumes should serve as a useful reference.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
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×Product details
 Date Published: January 2018
 format: Paperback
 isbn: 9781108414456
 length: 378 pages
 dimensions: 227 x 152 x 23 mm
 weight: 0.55kg
 contains: 1 b/w illus.
 availability: Available
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 A2module
20. The algebraic group Ḡ(n)
21. Endomorphisms of P(n) over A2
22. The Steinberg summands of P(n)
23. The dspike 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 4variable hit problem, I
30. The 4variable hit problem, II
Bibliography
Index of Notation for Volume 2
Index for Volume 2
Index of Notation for Volume 1
Index for Volume 1.
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