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Polynomials and the mod 2 Steenrod Algebra

Volume 2. Representations of GL (n,F2)


Part of London Mathematical Society Lecture Note Series

  • Date Published: November 2017
  • availability: Available
  • format: Paperback
  • isbn: 9781108414456

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About the Authors
  • 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.

    • Algebraic and combinatorial treatment of Steenrod algebra
    • Accessible to those without a background in topology
    • Largely self-contained with detailed proofs
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    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 Moreover, the material in Volume 2 using the cyclic splitting of P(n) is based in part upon the unpublished Ph.D. thesis of Helen Weaver … Much of the material covered has not hitherto appeared in book form, and these volumes should serve as a useful reference.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: November 2017
    • 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

    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
    Index of Notation for Volume 2
    Index for Volume 2
    Index of Notation for Volume 1
    Index for Volume 1.

  • Authors

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

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