The Gelfand-Kirillov dimension of a unitary highest weight module

Autor:	ZhanQiang Bai, Markus Hunziker
Rok vydání:	2015
Předmět:	Algebra Pure mathematics Degree (graph theory) Series (mathematics) Dimension (vector space) General Mathematics Gelfand–Kirillov dimension Nilpotent orbit Algebraic geometry Mathematics::Representation Theory Unitary state Mathematics Dual pair
Zdroj:	Science China Mathematics. 58:2489-2498
ISSN:	1869-1862 1674-7283
DOI:	10.1007/s11425-014-4968-y
Popis:	During the last decade, a great deal of activity has been devoted to the calculation of the Hilbert-Poincare series of unitary highest weight representations and related modules in algebraic geometry. However, uniform formulas remain elusive—even for more basic invariants such as the Gelfand-Kirillov dimension or the Bernstein degree, and are usually limited to families of representations in a dual pair setting. We use earlier work by Joseph to provide an elementary and intrinsic proof of a uniform formula for the Gelfand-Kirillov dimension of an arbitrary unitary highest weight module in terms of its highest weight. The formula generalizes a result of Enright and Willenbring (in the dual pair setting) and is inspired by Wang’s formula for the dimension of a minimal nilpotent orbit.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::a5f47403c3d74dd08f0c5aec4982a854 https://doi.org/10.1007/s11425-014-4968-y Zobrazit plný text záznamu Full text from SpringerLink