Separation of variables for U-q(sl(n+1))(+)

• Type: Article in International Scientific Journal
• Date: 2005

Authors

Lopes, SA (Author) FCUP

Journal

Title: Canadian Mathematical Bulletin

Vol. 48

Pages: 587-600

ISSN: 0008-4395

Publisher: Canadian Mathematical Society

Indexing

ISI Web of Knowledge - 2 Citations

Scopus - 2 Citations

Other information

Authenticus ID: P-00F-H95

DOI: 10.4153/cmb-2005-054-8

Abstract (EN): Let U-q(sl(n+1))(+) the positive part of the quantized enveloping algebra Uq(sl(n+1)). Using results of Alev-Dumas and Caldero related to the center of U-q(sl(n+1))(+) we show that this algebra is free over its center. This is reminiscent of Kostant's separation of variables for the enveloping algebra U (g) of a complex semisimple Lie algebra and also of an analogous result of Joseph-Letzter for the quantum algebra U-q(g). Of greater importance to its representation theory is the fact that U-q(sl(n+1))(+) is free over a larger polynomial subalgebra N in n variables. Induction from N to Uq(sl(n+1))(+) provides infinite-dimensional modules with good properties, including a grading that is inherited by submodules.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 14