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

Penkov, Ivan ; Zuckerman, Gregg

Canadian mathematical bulletin, Tome 50 (2007) no. 4, pp. 603-609

Résumé

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.

Détail

DOI : 10.4153/CMB-2007-059-5

Mots-clés : 17B10, 17B55