%0 Journal Article
%A Calixto Molina, Manuel
%T Generalized W∞ Higher-Spin Algebras and Symbolic Calculus on Flag Manifolds
%D 2006
%@ 0393-0440
%U http://hdl.handle.net/10317/507
%U arXiv:hep-th/0301200v3
%X 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 diffeomorphism-invariant
gauge field theories, like gauge theories of higher-extended objects, and non-linear sigma
models on flag manifolds.
%K Matemática Aplicada
%K Simetria Visasoro y W∞
%K Berezin y Cuantización geométrica
%K Operador de símbolo
%K Diformismo invariante QFT
%K Visasoro symmetry and W ∞
%K Berezin and geometric quantization
%K Operator symbol
%K Deformity invariant QFT
%~ GOEDOC, SUB GOETTINGEN