报告地点：翡翠科教楼B座1710室

举办单位：数学学院

报告一：Representations of the Sergeev superalgebra, queer immanants and Capelli identities

报告时间：10 月 22 日14:30–15:30

报  告  人：Prof. Alexander Molev

工作单位：The University of Sydney

报告简介:

We use the Jucys-Murphy elements to construct a complete set of primitive idempotents for the Sergeev superalgebra. We apply them to produce quantum immanants for the queer Lie superalgebra q_N as central elements of its universal enveloping algebra. We prove a universal Capelli identity for q_N and use it to calculate the images of the quantum immanants under the action of q_N in differential operators. We show that the Harish-Chandra images of the quantum immanants coincide with the factorial Schur Q-polynomials.

This is joint work with Iryna Kashuba and Vera Serganova.

报告人简介：

Alexander Molev, 悉尼大学教授，澳大利亚科学院院士，国际著名表示论专家，在 Yangian 代数、组合数学等诸多研究领域都作出了重要的贡献。2001 年获得澳大利亚数学会奖。在 Inventiones mathematicae，Dukemathematical journal，Advances in Mathematics，Comm. Math. Phys. 等国际知名期刊发表文章近百篇。

报告二：Quantum Casimir elements and Higher Capelli identities

报告时间：10 月 22 日15:45–16:45

报  告  人：刘明 特聘教授

工作单位：江汉大学

报告简介:

In 1996, Okounkov introduced quantum immanants which form a basis of the center of U(gl_n) and gave the Capelli identities corresponding to quantum immanants. Moreover, the Harish-Chandra images of quantum immanants are shifted Schur polynomials. In this talk, we will talk about the q-analogue of quantum immanants and the corresponding Capelli identities.

报告人简介：

刘明，江汉大学湖北省楚天学者特聘教授。主要研究方向为量子群与 Yangian 代数的表示理论。代表性成果发表在 Advances in Mathematics ,Communications in Mathematical Physics, Journal of Algebra 等国际知名期刊。主持国家自然科学基金面上项目 1 项，国家自然科学基金青年基金 1 项，广东省自然科学基金面上项目 1 项，参与国家自然科学基金重点项目 1 项。

报告三：Central elements for twisted quantum enveloping algebras

报告时间：10 月 22 日16:45–17:45

报  告  人：张健 教授

工作单位：华中师范大学

报告简介：

We study two approaches to the construction of central elements in twisted quantum enveloping algebras of orthogonal and symplectic types. The first approach is based on the fusion procedure, which yields central elements associated with arbitrary idempotents in Hecke algebras. The second approach relies on invariant tensors arising from quantum Schur–Weyl duality. Using this approach, we provide a unified construction of quantum Pfaffians and Hafnians and establish their centrality. Finally, we investigate the relationship between quantum Pfaffians and Sklyanin determinants.

报告人简介：

张健，华中师范大学教授。国家级人才计划入选者，2015年获华南理工大学博士学位，2016年至2020年先后在巴西圣保罗大学、中国台湾等地从事博士后工作。主要研究方向为李代数、量子群、表示论。在Adv.Math.,JLMS，Math.Z.等期刊发表学术论文二十余篇。

报告四: A class of Niho type four-valued cross-correlation functions of sequences with different lengths

报告时间：10月23日09:00–10:00

报  告  人：曾祥勇 教授

工作单位：湖北大学

报告简介:

Cross-correlation properties of m-sequences and their decimated sequences are an important research object of low correlation sequences. In this talk, for two positive integers n and k with n=2k, we investigate the cross-correlation function between a binary m-sequence u(t) of period 2^{n}-1 and its 2^{\gcd(s,k)}+1 short-period decimated sequences u(dt+l), where the decimation d=\frac{2^s}{2^s+1}(2^k-1)+1 satisfies 1<s<n and v_2(s)>v_2(k). The cross-correlation function is proved to be four-valued and its value distribution is completely determined. Several previously known binary cross-correlation functions are included in our result as special cases.

报告人简介：

曾祥勇，湖北大学二级教授，博士生导师。获国务院政府特殊津贴、全国密码算法设计竞赛（分组密码）三等奖、湖北省高等学校教学成果一等奖、湖北省自然科学奖一等奖和二等奖。主要研究领域为代数学、密码学和编码学，先后主持国家自然科学基金项目和国家重点研发计划课题10余项。

报告五：Higher-order quantum Casimir elements

报告时间：10月23日10:15–11:15

报  告  人：张洋 博士

工作单位：澳大利亚詹姆斯库克大学

报告简介：

Casimir elements play a central role in the representation theory of Lie algebras: they generate the centre of the universal enveloping algebra and act by scalar multiplication on every irreducible module. For quantum groups, the standard quadratic quantum Casimir has been known since the early days of the theory, but higher-order analogues---quantum counterparts of the classical Gelfand invariants---have remained less well understood.

In this talk, I will present recent work on the higher-order Casimir elements for quantum groups of classical types. I will explain how these elements generate the centre of the quantum group, and describe their Harish-Chandra images in terms of irreducible characters associated with hook partitions. This is joint work with Yanmin Dai.

报告人简介：

张洋，澳大利亚詹姆斯库克大学科学与工程学院讲师，悉尼大学博士。主要研究方向为李超代数、量子群和反射群的表示理论及其与几何、拓扑和组合数学的联系。代表性成果发表在 Advances in Mathematics、Communi-cations in Mathematical Physics、Journal of Algebra 等国际知名期刊。