This book examines the representation theory of the general linear groups, and reveals that there is a close analogy with that of the symmetric groups.
This book examines the representation theory of the general linear groups, and reveals that there is a close analogy with that of the symmetric groups.
Abstract; List of symbols; 1. Introduction; 2. Examples; 3. Gaussian polynomials; 4. Compositions of n; 5. Root subgroups of Gn; 6. Subgroups of Gn associated with compositions; 7. Coset representatives; 8. Subgroups of Gn used for induction; 9. Some idempotent elements of KGn; 10. The permutation module M ; 11. The Submodule Theorem; 12. A lower bound for the dimension of S ; 13. The Kernel Intersection Theorem for S(n-m,m); 14. Reordering the parts of ; 15. The Kernel Intersection Theorem; 16. Consequences of the Kernel Intersection Theorem; 17. Removing the first column from [ ]; 18. Isotropic spaces; 19. The prime divisors of Gaussian polynomials; 20. The composition factors of S(n-m,m); Acknowledgements; References.
Abstract; List of symbols; 1. Introduction; 2. Examples; 3. Gaussian polynomials; 4. Compositions of n; 5. Root subgroups of Gn; 6. Subgroups of Gn associated with compositions; 7. Coset representatives; 8. Subgroups of Gn used for induction; 9. Some idempotent elements of KGn; 10. The permutation module M ; 11. The Submodule Theorem; 12. A lower bound for the dimension of S ; 13. The Kernel Intersection Theorem for S(n-m,m); 14. Reordering the parts of ; 15. The Kernel Intersection Theorem; 16. Consequences of the Kernel Intersection Theorem; 17. Removing the first column from [ ]; 18. Isotropic spaces; 19. The prime divisors of Gaussian polynomials; 20. The composition factors of S(n-m,m); Acknowledgements; References.
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