Differential operators and highest weight representations / [electronic resource] Mark G. Davidson, Thomas J. Enright, Ronald J. Stanke.

By: Davidson, Mark G, 1955-Contributor(s): Enright, Thomas J | Stanke, Ronald J, 1954-Material type: TextTextSeries: Memoirs of the American Mathematical Society ; v. 455Publication details: Providence, RI : American Mathematical Society, c1991Description: 1 online resource (iv, 102 p. : ill.)ISBN: 9781470408817 (online)Subject(s): Semisimple Lie groups | Representations of groups | Differential operatorsAdditional physical formats: Differential operators and highest weight representations /DDC classification: 510 s | 512/.55 LOC classification: QA3 | .A57 no. 455 | QA387Online resources: Contents | Contents
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
Item type: E-BOOKS
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Includes bibliographical references and index.

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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Electronic reproduction. Providence, Rhode Island : American Mathematical Society. 2012

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