Generalized W∞ Higher-Spin Algebras and Symbolic Calculus on Flag Manifolds
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Calixto Molina, ManuelÁrea de conocimiento
Matemática AplicadaFecha de publicación
2006-02Editorial
Elsevier ScienceCita bibliográfica
MANUEL CALIXTO, Manuel. Generalized W∞ Higher-Spin Algebras and Symbolic Calculus on Flag Manifolds. Journal of Geometry and Physics, 56 (2): 143-174, Febrero 2006. ISSN 0393-0440Palabras clave
Simetria Visasoro y W∞Berezin y Cuantización geométrica
Operador de símbolo
Diformismo invariante QFT
Visasoro symmetry and W ∞
Berezin and geometric quantization
Operator symbol
Deformity invariant QFT
Resumen
We study a new class of infinite-dimensional Lie algebras W1(N+,N−) generalizing
the standard W1 algebra, viewed as a tensor operator algebra of SU(1, 1) in a grouptheoretic framework. Here we interpret W1(N+,N−) either as an infinite continuation
of the pseudo-unitary symmetry U(N+,N−), or as a “higher-U(N+,N−)-spin extension”
of the diffeomorphism algebra diff(N+,N−) of the N = N++N− torus U(1)N. We highlight
this higher-spin structure of W1(N+,N−) by developing the representation theory
of U(N+,N−) (discrete series), calculating higher-spin representations, coherent states
and deriving K¨ahler structures on flag manifolds. They are essential ingredients to define operator symbols and to infer a geometric pathway between these generalized W1 symmetries and algebras of symbols of U(N+,N−)-tensor operators. Classical limits (Poisson brackets on flag manifolds) and quantum (Moyal) deformations are also discussed.
As potential applications, we comment on the formulation of diffeom ...
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