科研之友
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摘要
We will give a representation-theoretic proof for the multiplication formula in the Ringel-Hall algebra h(Delta)(n) of a cyclic quiver Delta(n). As a first application, we see immediately the existence of Hall polynomials for cyclic quivers, a fact established by J. Y. Guo and C. M. Ringel, and derive a recursive formula to compute them. We will further use the formula and the construction of a monomial basis for h(Delta)(n) given by Deng, Du, and Xiao together with the double Ringel-Hall algebra realisation of the quantum loop algebra U-v((gl) over cap (n)) given by Deng, Du, and Fu to develop some algorithms and to compute the canonical basis for U-v(+)((gl) over cap (n)). As examples, we will show explicitly the part of the canonical basis associated with modules of Lowey length at most 2 for the quantum group U-v ((gl) over cap (2)).
- 出版日期2018-8
- 单位北京化工大学
