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

Ivan Penkov, Gregg Zuckerman

• 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