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Differential operators and highest weight representations

About this Title

Mark G. Davidson, Thomas J. Enright and Ronald J. Stanke

Publication: Memoirs of the American Mathematical Society
Publication Year 1991: Volume 94, Number 455
ISBNs: 978-0-8218-2509-9 (print); 978-1-4704-0881-7 (online)
MathSciNet review: 1081660
MSC: Primary 22E47

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Table of Contents


  • 0. Introduction and summary of results
  • 1. Vector bundles and algebraic conventions
  • 2. Conjugate pairings and reproducing kernels
  • 3. $\mathfrak {k}$-irreducibility of the system of differential operators
  • 4. $\mathfrak {p}_+$-cohomology for the exceptional groups
  • 5. Notational conventions and a lemma
  • 6. The cone decomposition
  • 7. The oscillator representation, harmonic polynomials and associated affine varieties
  • 8. Young products and a refinement of the factorization theorem
  • 9. The fundamental system of differential operators
  • 10. Explicit forms of the systems of differential operators for the classical groups
  • 11. The ladder representation examples
  • 12. $K_{\mathbb {C}}$-orbits in $\mathfrak {p}_+$ and the Wallach representations

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