Construction of Generalized Harish-Chandra Modules with Arbitrary Minimal mathfrak k-Type

• Autores: Ivan Penkov, Gregg Zuckerman
• Localización: Canadian mathematical bulletin, ISSN 0008-4395, Vol. 50, Nº 4, 2007, págs. 603-609
• Idioma: inglés
• DOI: 10.4153/cmb-2007-059-5
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• Resumen

  • Let mathfrak g be a semisimple complex Lie algebra and mathfrac k \subset mathfrak g be any algebraic subalgebra reductive in mathfrak g. For any simple finite dimensional mathfrak k-module V, we construct simple (mathfrak g, mathfrak k)-modules M with finite dimensional mathfrak k-isotypic components such that V is a mathfrak k-submodule of M and the Vogan norm of any simple mathfrak k-submodule V' \subset M, V' \not\simeq V, is greater than the Vogan norm of V. The (mathfrak g, mathfrak k)-modules M are subquotients of the fundamental series of (mathfrak g, mathfrak k)-modules