Cent U(n) and a construction of Lipsman-Wolf

Bertram Kostant

Published 2011-01-12Version 1

Let $G$ be a complex simply-connected semisimple Lie group and let $\g= \hbox{\rm Lie}\,G$. Let $\g = \n_- +\hh + \n$ be a triangular decomposition of $\g$. The authors in [LW] introduce a very nice representation theory idea for the construction of certain elements in $\hbox{\rm cent}\,U(n)$. A key lemma in [LW] is incorrect but the idea is in fact valid. In our paper here we modify the construction so as to yield the desired elements in $\hbox{\rm cent}\,U(\n)$.