Nicht lieferbar
Differential Operators and Highest Weight Representation
Versandkostenfrei!
Nicht lieferbar
This work concerns the representation theory of semisimple Lie groups. From the algebraic perspective, the theory of unitarizable highest weight modules is highly developed. The classification was given in 1981, and, more recently, even the character and nilpotent cohomology formulas have been determined for G of classical type. However, from the analytic point of view, as originally presented by Harish-Chandra, unitarizable highest weight modules occur as subspaces of certain spaces of vector-valued polynomials, or, equivalently, as subspaces of holomorphic sections for vector bundles on G/K....
This work concerns the representation theory of semisimple Lie groups. From the algebraic perspective, the theory of unitarizable highest weight modules is highly developed. The classification was given in 1981, and, more recently, even the character and nilpotent cohomology formulas have been determined for G of classical type. However, from the analytic point of view, as originally presented by Harish-Chandra, unitarizable highest weight modules occur as subspaces of certain spaces of vector-valued polynomials, or, equivalently, as subspaces of holomorphic sections for vector bundles on G/K. The main results of this book offer characterizations of unitary highest weight representations as solutions to systems of differential operators.
Table of contents:
Vector bundles and algebraic conventions; Conjugate pairings and reproducing kernels; e-irreducibility of the system of differential operators; p+-cohomology for the exceptional groups; Notational conventions and lemma; The cone decomposition; The oscillator representation, harmonic polynomials and associated affine varieties; Young products and refinement of the factorization theorem; The fundamental system of differential operators; Explicit forms of the systems of differential operators for the classical groups; The ladder representation examples; KC-orbits in p+ for the Wallach representations.
Table of contents:
Vector bundles and algebraic conventions; Conjugate pairings and reproducing kernels; e-irreducibility of the system of differential operators; p+-cohomology for the exceptional groups; Notational conventions and lemma; The cone decomposition; The oscillator representation, harmonic polynomials and associated affine varieties; Young products and refinement of the factorization theorem; The fundamental system of differential operators; Explicit forms of the systems of differential operators for the classical groups; The ladder representation examples; KC-orbits in p+ for the Wallach representations.