Hilbert series, Howe duality and branching for classical groups
The authors consider an extension of the Littlewood restriction rule which covers all pertinent parameters and reduces to the original one under Littlewood's hypothesis. Two formulas are derived for the Gelfand-Kirillov dimension of any unitary highest weight representation occuring in the dual pair setting, one in terms of the dual pair index and the other in terms of the highest weight. They define a class of unitary highest weight representations and show that each of these representations has a Hilbert series. In Section 1 they present the main results of this article, most of which were announced in [\textit{T. J. Enright} and \textit{J. F. Willenbring}, Proc. Natl. Acad. Sci. USA 100, No. 2, 434--437 (2003; Zbl 1065.22008)]. In the following sections they give details of the proofs of these results and some remarks. These descriptions are too deep and complicated to explain here.
unitarizable highest weight representations
scientific article; zbMATH DE number 2123897