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

Open Access article
 Printed: Dec 2007
  • Ivan Penkov
  • Gregg Zuckerman
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Let $\mathfrak g$ be a semisimple complex Lie algebra and $\k\subset\g$ 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 $\k$-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.
MSC Classifications: 17B10, 17B55 show english descriptions Representations, algebraic theory (weights)
Homological methods in Lie (super)algebras
17B10 - Representations, algebraic theory (weights)
17B55 - Homological methods in Lie (super)algebras

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