Canonical bases and quantum coordinate algebras

Some filtrations of the tensor product of a highest weight module and a lowest weight module over quantum group Uq(g)Uq(g) are constructed in [1] and one can use them to define a two-sided ideal of the modified quantized enveloping algebra. It is shown that the quotient algebra inherits a canonical basis from the modified quantized enveloping algebra and is dual to the quantum coordinate algebra defined by Kashiwara for a symmetrizable Kac–Moody algebra gg.