The quantum Casimir operators of $\Uq$ and their eigenvalues

Details The quantum Casimir operators of $\Uq$ and their eigenvalues The quantum Casimir operators of $\Uq$ and their eigenvalues

2010-03-19

arxiv.org/abs/1003.3729v1

Mathematics

Quantum Algebra

10 pages

Scientific paper

We show that the quantum Casimir operators of the quantum linear group constructed in early work of Bracken, Gould and Zhang together with one extra central element generate the entire center of $\Uq$. As a by product of the proof, we obtain intriguing new formulae for eigenvalues of these quantum Casimir operators, which are expressed in terms of the characters of a class of finite dimensional irreducible representations of the classical general linear algebra.

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