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math.RT2015★ 2 cited
An insight into the description of the crystal structure for Mirković-Vilonen polytopes
Yong Jiang, Jie Sheng
We study the description of the crystal structure on the set of Mirković-Vilonen polytopes. Anderson and Mirković defined an operator and conjectured that it coincides with the Kas…
math.RT2009
Tame quivers and affine enveloping algebras
Yong Jiang, Jie Sheng
Let be an affine Kac-Moody algebra with symmetric Cartan datum, be the maximal nilpotent subalgebra of . By the Hall algebra approac…
math.RT2009
The elements in crystal bases corresponding to exceptional modules
Yong Jiang, Jie Sheng, Jie Xiao
According to the Ringel-Green Theorem([G],[R1]), the generic composition algebra of the Hall algebra provides a realization of the positive part of the quantum group. Furthermore,…