Shuffle algebras and their integral forms: specialization map approach

发布时间：2025-04-02 作者：浏览次数：

Speaker:	胡越	DateTime:	2025年4月18日（周五）下午15：00-16：00
Brief Introduction to Speaker: 胡越，博士毕业于中国科学院数学与系统科学研究院，先后在Skolkovo Institute of Science and Technology以及清华大学丘成桐数学科学中心从事博士后研究，现任职于北京邮电大学。主要研究兴趣为Quantum affine algebras and shuffle algebras。		Place:	国交2号楼315会议室
Abstract:Shuffle algebras were introduced by Feigin-Odesskii, whose benefit is that it provides a combinatorial model for the positive subalgebra of quantum loop algebras in new Drinfeld realization. Enriquez conjectured, and recently proved by Negut-Tsymbaliuk, that the images of this algebra embedding are governed by certain wheel conditions. Another approach to address Enriquez conjecture is by utilizing certain specialization maps. For type A, this was accomplished through works of Feigin, Negut, and Tsymbaliuk. In this talk, we shall generalize the specialization map approach to types B,C,D,G. As a significant application, we also construct a family of PBW bases for the positive subalgebra of quantum loop algebras in these types, as well as their integral forms.