報告題目：Partitions in representation theory and integrable systems
報 告 人：李傳忠 教授 山東科技大學
所在單位：山東科技大學
報告時間：2024年8月24日 9:00-10:00
報告地點：吉林大學數學樓第6研讨室
校内聯系人：生雲鶴 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).
報告人簡介：李傳忠，山東科技大學教授、博士生導師、山東省泰山學者。2011年博士畢業于中國科學技術大學伟德线上平台，美國俄亥俄州立大學聯合培養博士。現擔任中國高等教育學會教育數學專業委員會理事，山東省大數據研究會理事。主要從事數學物理方向的研究工作。2015 年入選甯波市領軍和拔尖人才培養工程。2017年入選浙東青年學者計劃。2020年入選山東省泰山學者青年專家。主持國家自然科學基金面上項目2項和青年基金項目1項。以第一作者或唯一通訊作者身份在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.等期刊發表 SCI論文120篇。
