Differential Operators and Highest Weight Representations.
Davidson, Mark G.
Differential Operators and Highest Weight Representations. - 1st ed. - 1 online resource (111 pages) - Memoirs of the American Mathematical Society ; v.94 . - Memoirs of the American Mathematical Society .
Intro -- Table of Contents -- 0 Introduction and Summary of Results -- 1 Vector Bundles and Algebraic Conventions -- 2 Conjugate Pairings and Reproducing Kernels -- 3 k-Irreducibility of the System of Differential Operators -- 4 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 KC-Orbits in p+ and the Wallach Representations -- Notational Index -- Bibliography.
9781470408817
Semisimple Lie groups.
Representations of groups.
Differential operators.
Electronic books.
QA387 -- .D385 1991eb
512/.55
Differential Operators and Highest Weight Representations. - 1st ed. - 1 online resource (111 pages) - Memoirs of the American Mathematical Society ; v.94 . - Memoirs of the American Mathematical Society .
Intro -- Table of Contents -- 0 Introduction and Summary of Results -- 1 Vector Bundles and Algebraic Conventions -- 2 Conjugate Pairings and Reproducing Kernels -- 3 k-Irreducibility of the System of Differential Operators -- 4 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 KC-Orbits in p+ and the Wallach Representations -- Notational Index -- Bibliography.
9781470408817
Semisimple Lie groups.
Representations of groups.
Differential operators.
Electronic books.
QA387 -- .D385 1991eb
512/.55