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Construction of Generalized Harish-Chandra Modules with Arbitrary Minimal
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Published online by Cambridge University Press: 20 November 2018
Abstract
Let $\mathfrak{g}$ be a semisimple complex Lie algebra and
$\mathfrak{k}\,\subset \mathfrak{g}$ be any algebraic subalgebra reductive in
$\mathfrak{g}$. For any simple finite dimensional
$\mathfrak{k}$-module
$V$, we construct simple
$\left( \mathfrak{g},\mathfrak{k} \right)$-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
$V\prime \subset M,V\prime \ne \,V$, is greater than the Vogan norm of
$V$. The
$\left( \mathfrak{g},\mathfrak{k} \right)$-modules
$M$ are subquotients of the fundamental series of
$\left( \mathfrak{g},\mathfrak{k} \right)$-modules.
- Type
- Research Article
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- Copyright
- Copyright © Canadian Mathematical Society 2007
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