PERMUTATION GROUPS

The following sections are included:

• Multiplication of Permutations

  • Permutations

  • Cycles

  • Classes in a Permutation Group

  • Alternating Subgroups

  • Transposition of Two Neighbored Objects

• Young Patterns, Young Tableaux, and Young Operators

  • Young Patterns

  • Young Tableaux

  • Young Operators

  • Fundamental Property of Young Operators

  • Products of Young Operators

• Irreducible Representations of S_n

  • Primitive Idempotents in the Group Algebra of S_n

  • Orthogonal Primitive Idempotents of S_n

  • Calculation of Representation Matrices for S_n

  • Calculation of Characters by Graphic Method

  • The Permutation Group S₃

  • Inner Product of Irreducible Representations of S_n

• Real Orthogonal Representation of S_n

• Outer Product of Irreducible Representations of S_n

  • Representations of S_n+m and Its Subgroup S_n ⊗ S_m

  • Littlewood–Richardson Rule

• Exercises