A parameterization of the canonical bases of affine modified quantized enveloping algebras (Q266192)

The authors study the problem of construction the canonical bases of affine modified quantized enveloping algebras. The modified quantized enveloping algebra \(\dot{\mathbf{U}}\) is obtained from the classical quantized enveloping algebra \(\mathbf U\) by modifying its Cartan part. Let \(\Delta\) be a Dynkin or affine quiver and let \(\mathcal R\) be the \(T^2\)-orbit category of the bounded derived category of \(\Delta\), where \(T\) is the translation functor. With \(\mathcal R\) the authors associate a set \(\widetilde{\mathcal M}\) and prove that there is a bijection between \(\widetilde{\mathcal M}\) and the canonical basis \(\dot{\mathbf B}\) of the modified quantized enveloping algebra \(\dot{\mathbf U}\) of type \(\Delta\).