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sagan b symmetric group 1991

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Textbook in PDF format Preface List of Symbols Group Representations Fundamental Concepts Matrix Representations G-modules and the Group Algebra Reducibility Complete Reducibility and Maschke's Theorem G-homomorphisms and Schur’s Lemma Commutant and Endomorphism Algebras Group Characters Inner Products of Characters Decomposition of the Group Algebra Tensor Products Again Restricted and Induced Representations Exercises Representations of the Symmetric Group Young Subgroups, Tableaux, and Tabloids Dominance and Lexicographic Ordering Specht Modules The Submodule Theorem Standard Tableaux and a Basis for S^lambda Garnir Elements Young’s Natural Representation The Branching Rule The Decomposition of M^mu The Semistandard Basis for Hom(S^lambda, M^mu) Kostka Numbers and Young’s Rule Exercises Combinatorial Algorithms The Hook Formula The Determinantal Formula The Robinson-Schensted Algorithm Column Insertion Increasing and Decreasing Subsequences The Knuth Relations Subsequences Again Viennot’s Geometric Construction Schützenberger’s Jeu de Taquin Dual Equivalence Evacuation Exercises Symmetric Functions Introduction to Generating Functions The Hillman-Grassl Algorithm The Ring of Symmetric Functions Schur Functions The Jacobi-Trudi Determinants Other Deﬁnitions of the Schur Function The Characteristic Map Knuth’s Algorithm The Littlewood-Richardson Rule The Murnaghan-Nakayama Rule Exercises Bibliography Index

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Sagan B. The Symmetric Group 1991.pdf 8.1 MB

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sagan b symmetric group 1991