报告题目：Partitions in representation theory and integrable systems
报 告 人：李传忠 教授 山东科技大学
所在单位：山东科技大学
报告时间：2024年8月24日 9:00-10:00
报告地点：吉林大学数学楼第6研讨室
校内联系人：生云鹤 shengyh@jlu.edu.cn
摘要：In this talk, we will review our studies in different directions of partitions in representation theory related to integrable systems.
1. The additional symmetries of integrable systems constitute virasoro algebra, W algebra, Block algebra, quantum torus Lie algebra and so on.
2. The partitions have one to one correspondence to Young diagrams which produces schur function as the tau function of KP systems. In this direction, we considered the double partitions and did a series of studies on the twisted Jacobi-Trudi formula which is called universal character.
3. The partitions connect with permutation group, chord diagram, pipedream, Le-diagrams which all connect with soliton graph of KP systems. In this direction, we considered the combinatorics inside the line-soliton solutions of KP type systems.
4. The symbol of partitions is used to describe the Springer correspondence for the classical groups by Lusztig. We refine the explanation that the S-duality maps of the rigid surface operators are symbol preserving maps. We clear up cause of the mismatch problem of the total number of the rigid surface operators between the B type and C type Lie algebraic theories. And we construct all the B/C rigid surface operators which can not have a dual. A classification of the problematic surface operators is made. This work was published in Commun. Math. Phys. (2024). Also we proved the conjecture of Witten that the symbol invariant of partitions is equivalent to the fingerprint invariant of partitions for the rigid surface operators (see arxiv).
报告人简介：李传忠，山东科技大学教授、博士生导师、山东省泰山学者。2011年博士毕业于中国科学技术大学数学学院，美国俄亥俄州立大学联合培养博士。现担任中国高等教育学会教育数学专业委员会理事，山东省大数据研究会理事。主要从事数学物理方向的研究工作。2015 年入选宁波市领军和拔尖人才培养工程。2017年入选浙东青年学者计划。2020年入选山东省泰山学者青年专家。主持国家自然科学基金面上项目2项和青年基金项目1项。以第一作者或唯一通讯作者身份在Commun. Math. Phys., Phys. Lett. B, J Nonl. Sci., Nuc. Phys. B, Lett. Math. Phys., Stud. Appl. Math., J. Alg. Comb., Phys. D, Phys. Rev. E, J. Phys. A, J. Math. Phys., J. Geom. Phys.等期刊发表 SCI论文120篇。
