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Irreducible characters of GL(n, q) and vertex operators

发布时间:2024-04-08 作者: 浏览次数:
Speaker: 景乃桓 DateTime: 2024年4月14日(周日)上午9:30-11:00
Brief Introduction to Speaker:

景乃桓,美国北卡州立大学教授,博士生导师。“CJ学者”讲座教授,国家杰出青年基金(B类)获得者,德国洪堡学者,美国富尔布莱特学者。主要从事无限维李代数、量子群、表示论、代数组合和量子计算方面的研究工作。特别地,与耶鲁大学Frenkel教授合作,首次构造仿射量子代数的顶点表示,是该领域的开创性工作,发表在数学顶尖刊物Invent Math.上;研究对称多项式函数时引入的“景氏算子”,被著名数学家MacDonald评论为对称函数的新研究方法。在国际著名期刊上发表论文两百多篇,编辑著作5部,主持多项国家自然科学基金,其中重点项目一项。

Place: 6号楼213报告厅
Abstract:Irreducible characters of the finite group GL(n, q) were determined by Green in a remarkable paper that has influenced representation theory greatly. In this talk, I will discuss a vertex algebraic approach to construct and compute all complex irreducible characters of GL(n, q). Green's theory is recovered and enhanced under the realization of the Grothendieck ring of representations $R(G)=\bigoplus_{n\geq 0} R(GL(n,q))$ as two isomorphic Fock spaces. Under this picture, the irreducible characters are realized by the Bernstein vertex operators for Schur functions, the characteristic functions of the conjugacy classes are realized by the vertex operators for the Hall-Littlewood functions, and the character table is completely given by matrix coefficients of vertex operators of these two types. This offers a simplification to identify the Fock space R(G) as the Hall algebra of symmetric functions. We will also discuss how to compute the characters in general. This is joint work with Y...