• Preface (7)
• Introduction (9)
• Contents (12)
• 1 First Steps (15)
  • 1.1 Permutations and Groups (15)
  • 1.2 Group Actions and Representations (18)
  • 1.3 More About the Symmetric Group (20)
  • 1.4 More Groups and Subgroups (22)
  • 1.5 Group Homomorphisms and More About Representations (25)
  • 1.6 Representations on Function Spaces (29)
  • 1.7 Hints and Additional Comments (31)
• 2 Polynomials, Subspaces and Subrepresentations (39)
  • 2.1 Polynomials (39)
  • 2.2 Subspaces and Subrepresentations (41)
  • 2.3 Partitions and More Subrepresentations (41)
  • 2.4 Vector Space Direct Sums (43)
  • 2.5 Projection Maps (45)
  • 2.6 Irreducible Subspaces (46)
  • 2.7 Hints and Additional Comments (48)
• 3 Intertwining Maps, Complete Reducibility, and Invariant Inner Products (52)
  • 3.1 Intertwining Maps (52)
  • 3.2 Complete Reducibility (55)
  • 3.3 Invariant Inner Products and Another Proof of Complete Reducibility (57)
  • 3.4 Dual Spaces and Contragredient Representations (60)
  • 3.5 Hints and Additional Comments (62)
• 4 The Structure of the Symmetric Group (73)
  • 4.1 Cycles and Cycle Structure (73)
  • 4.2 Generators and Parity (74)
  • 4.3 Conjugation and Conjugacy Classes (77)
  • 4.4 Hints and Additional Comments (78)
• 5 Sn-Decomposition of Polynomial Spaces for n=1,2,3 (79)
  • 5.1 S1 (79)
  • 5.2 S2 (79)
  • 5.3 S3 (80)
  • 5.4 Isotypic Subspaces and Multiplicities (83)
  • 5.5 Hints and Additional Comments (85)
• 6 The Group Algebra (88)
  • 6.1 Version One (88)
  • 6.2 Version Two (90)
  • 6.3 Hints and Additional Comments (92)
• 7 The Irreducible Representations of Sn: Characters (95)
  • 7.1 Characters and Class Functions (95)
  • 7.2 Characters of S3 (98)
  • 7.3 Orthogonality of Characters, Bases (99)
  • 7.4 Another Look (106)
  • 7.5 Hints and Additional Comments (109)
• 8 The Irreducible Representations of Sn: Young Symmetrizers (112)
  • 8.1 Partitions Again: Young Tableaux (112)
  • 8.2 Orderings on Partitions (113)
  • 8.3 Young Symmetrizers (114)
  • 8.4 Construction of Irreducible Representations in C[Sn] (118)
  • 8.5 More Representations (125)
  • 8.6 Hints and Additional Comments (127)
• 9 Cosets, Restricted and Induced Representations (133)
  • 9.1 Restriction (133)
  • 9.2 Quotient Spaces (134)
  • 9.3 Cosets (135)
  • 9.4 Coset Representations of a Group (138)
  • 9.5 Induced Representations: Version One (139)
  • 9.6 Matrix Realizations and Characters of Induced Representations (142)
  • 9.7 Construction of Induced Representations (143)
  • 9.8 Frobenius Reciprocity (144)
  • 9.9 Induced Representations: Version Two (145)
  • 9.10 Hints and Additional Comments (148)
• 10 Direct Products of Groups, Young Subgroups and Permutation Modules (161)
  • 10.1 Direct Products of Groups (161)
  • 10.2 Young Subgroups and Permutation Modules (163)
  • 10.3 Decomposition of Polynomial Spaces into Permutation Modules (165)
  • 10.4 More Permutation Modules: Tabloids and Polytabloids (166)
  • 10.5 Hints and Additional Comments (170)
• 11 Specht Modules (173)
  • 11.1 Construction of Specht Modules (173)
  • 11.2 Irreducibility of Specht Modules (174)
  • 11.3 Inequivalence of Specht Modules (176)
  • 11.4 The Standard Basis for Specht Modules (177)
    • 11.4.1 Linear Independence (178)
    • 11.4.2 Span (180)
    • 11.4.3 A Straightening Algorithm (181)
  • 11.5 Application to Polynomial Spaces (188)
  • 11.6 Hints and Additional Comments (189)
• 12 Decomposition of Young Permutation Modules (195)
  • 12.1 Generalized and Semistandard Young Tableaux (195)
  • 12.2 The Space C[Tλμ] and Its Equivalence to C[Tμ] (197)
  • 12.3 The Space HomC[Sn](Sλ, C[Tλμ]) (199)
  • 12.4 Column Equivalence and Ordering (202)
  • 12.5 The Semistandard Basis for Hom C[Sn](Sλ, Mμ) (203)
  • 12.6 Young's Rule (208)
  • 12.7 Hints and Additional Comments (209)
• 13 Branching Relations (217)
  • 13.1 The Hook Length Formula (217)
  • 13.2 Branching Relations (222)
  • 13.3 Hints and Additional Comments (228)
• Bibliography (232)
• Index (234)