主持人：胡乃红
报告人简介：
胡红梅，上海海事大学理学院副教授。主要从事量子群的结构(解决了1995年关于量子群结构的Majid猜想），近年来从事量子群不变量理论以及素特征域上(super)Yangians结构等研究工作，相关代表性成果发表在J. Lond. Math. Soc., Lett. Math. Phys., Isarel J. Math., Sci. Math. China, J. Algebra, Math. Research Lett., J. Math. Phys.等杂志上.
报告摘要：
The quantum symmetric algebra S_q(V) of the 7-dimensional simple U_q(G_2)-module V is not a flat deformation of the symmetric algebra of V. We decompose S_q(V) at generic q into a direct sum of simple U_q(G_2)-submodules, and determine their multiplicities. We construct a finite set of explicit generators for the subalgebra consisting of U_q(G_2)-invariants of the tensor product algebra S_q(V)}^{\otimes m} endowed with a braided multiplication defined by using the universal R-matrix.This result in particular enables one to describe the subspace of invariants of any tensor power of V, thus may be regarded as a noncommutative analogue of the first fundamental theorem of invariant theory forU_q(G_2).This is a joint work with Prof. Zhang Ruibin.
