Artículo
Quasifinite representations of classical Lie subalgebras of W∞, p
Fecha de publicación:
07/2013
Editorial:
American Institute Of Physics
Revista:
Journal Of Mathematical Physics
ISSN:
0022-2488
Idioma:
Inglés
Tipo de recurso:
Artículo publicado
Clasificación temática:
Resumen
We show that there are exactly two anti-involutions σ± of the algebra of differential operators on the circle that are a multiple of p(t∂t) preserving the principal gradation (p∈C[x]p∈C[x] non-constant). We classify the irreducible quasifinite highest weight representations of the central extension Dˆ±pD̂p± of the Lie subalgebra fixed by −σ±. The most important cases are the subalgebras Dˆ±xD̂x± of W∞ that are obtained when p(x) = x. In these cases, we realize the irreducible quasifinite highest weight modules in terms of highest weight representation of the central extension of the Lie algebra of infinite matrices with finitely many nonzero diagonals over the algebra C[u]/(um+1)C[u]/(um+1) and its classical Lie subalgebras of C and D types.
Palabras clave:
Quasifinite
,
Lie Superalgebra
Archivos asociados
Licencia
Identificadores
Colecciones
Articulos(CIEM)
Articulos de CENT.INV.Y ESTUDIOS DE MATEMATICA DE CORDOBA(P)
Articulos de CENT.INV.Y ESTUDIOS DE MATEMATICA DE CORDOBA(P)
Citación
Garcia, José Ignacio; Liberati, Jose Ignacio; Quasifinite representations of classical Lie subalgebras of W∞, p; American Institute Of Physics; Journal Of Mathematical Physics; 54; 7-2013
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