Capelli's Identity - Contents

Contents

  • 1 Statement
  • 2 Relations with representation theory
    • 2.1 Case m = 1 and representation Sk Cn
      • 2.1.1 Capelli identity for m = 1
    • 2.2 The universal enveloping algebra and its center
    • 2.3 General m and dual pairs
  • 3 Generalizations
    • 3.1 Turnbull's identity for symmetric matrices
    • 3.2 The Howe–Umeda–Kostant–Sahi identity for antisymmetric matrices
    • 3.3 The Caracciolo–Sportiello–Sokal identity for Manin matrices
    • 3.4 The Mukhin–Tarasov–Varchenko identity and the Gaudin model
      • 3.4.1 Statement
      • 3.4.2 The Gaudin quantum integrable system and Talalaev's theorem
    • 3.5 Permanents, immanants, traces – "higher Capelli identities"
      • 3.5.1 Turnbull's identity for permanents of antisymmetric matrices
  • 4 References
    • 4.1 Inline
    • 4.2 General

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