Representations of GL (n,F2)
著者
書誌事項
Representations of GL (n,F2)
（London Mathematical Society lecture note series, 442 . Polynomials and the mod 2 Steenrod algebra / Grant Walker,
Cambridge University Press, 2018
- : pbk
大学図書館所蔵 件 / 全35件
-
該当する所蔵館はありません
- すべての絞り込み条件を解除する
注記
Set ISBN for "Polynomials and the mod 2 Steenrod algebra": 9781108414067
Includes bibliographical references (p. 335-346) and indexes
内容説明・目次
内容説明
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.
目次
- 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 G(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.
「Nielsen BookData」 より
