题目:Drinfeld double of deformed quantum algebras 摘要: We provide a deformation, f_{\alpha, \beta} , of Lusztig algebra f. Various quantum algebras in literature, including half parts of two-parameter quantum algebras, quantum superalgebras, and multi-parameter quantum algebras/superalgebras, are all specializations of f_{\alpha, \beta} . Moreover, f_{\alpha, \beta} is isomorphic to Lusztig algebra f up to a twist. As a consequence, half parts of those quantum algebras are isomorphic to Lusztig algebra f over a big enough ground field up to certain twists. We further construct the entire algebra U _{\beta, \xi} by Drinfeld double construction. As special cases, above quantum algebras all admit a Drinfeld double construction under certain assumptions. This is a joint work with Junjing Xing. 报告人简介:樊赵兵,哈尔滨工程大学数学科学学院教授,博士生导师,国际交流与合作处处长,黑龙江杰出青年基金获得者。2012年于美国堪萨斯州立大学获博士学位,研究方向为几何表示论,主要从事与量子群、Hall代数、quiver表示和Character Sheaf等相关问题的研究。在Mem. Amer. Math. Soc., Comm. Math. Phys., Trans. Amer. Math. Soc., Int. Math. Res. Not., J. Algebra等国际高水平期刊上发表学术论文近二十篇,主持国家自然科学基金面上项目一项。
题目:Application of Schur-Weyl duality to Springer theory 摘要: We give the realization of Schur-Weyl duality of the symmetric pair by using the Springer theory of type B and C, and give the decomposition of the tensor space as bimodule. As an application, we can give the number of irreducible components of the springer fiber. 报告人简介:马海涛,博士毕业于华南理工大学,现在哈尔滨工程大学担任讲师,主要从事几何表示论方面的研究,具体是量子对称对的Schur-Weyl对偶的几何实现以及Cluster代数方面的研究,目前完成并在国内外重要刊物发表论文多篇。
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