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

Abstract

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.