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memo_has_moved_text();Differential operators and highest weight representations

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)
DOI: http://dx.doi.org/10.1090/memo/0455
MathSciNet review: 1081660
MSC: Primary 22E47

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Chapters

• 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