Canonical bases and quantum coordinate ring

Details Canonical bases and quantum coordinate ring Canonical bases and quantum coordinate ring

2010-02-25

arxiv.org/abs/1002.4701v1

Mathematics

Quantum Algebra

22 pages

Scientific paper

Some filtrations of the tensor product of a highest weight module and a lowest weight module over quantum group $U_q(\mathfrak g)$ are constructed in \cite{LZ:2009} and one can use them to define some ideals of the modified quantized enveloping algebra. It is shown that the quotient algebras inherit canonical bases from the modified quantized enveloping algebra and are dual to the quantum coordinate ring defined by Kashiwara for symmetrizable Kac-Moody algebra $\mathfrak g$.

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