学术报告（8.12）：杜杰 The q-Schur algebra of type D
报告人： 杜杰教授 (University of New South Wales, Australia)
报告时间：2024年 8月12日 下午16:00-17:00
报告地点：维格堂105
摘要： When I. Schur used representations of the symmetric group Sr to determine polynomial representations of the complex general linear group GLn(C), certain finite-dimensional algebras, known as Schur algebras, played a bridging role between the two. The well-known Schur duality summarizes the relation between the representations of GLn(C) and Sr. Over almost a hundred years, this duality has profoundly influenced representation theory and has evolved in various forms such as the Schur-Weyl duality, Schur-Weyl-Brauer duality, Schur-Weyl-Sergeev duality, and so on.
In this talk, I will discuss latest development, which I call the Schur-Weyl-Hecke duality, initiated by Huanchen Bao and Weiqiang Wang in their study of quantum symmetric pairs and canonical basis theory. This duality connects the i-quantum groups U^j(n) and U^i(n) to the Hecke algebras of types B and C, respectively, and has many applications. However, in the type D case, such a duality, first attempted by Fan and Li, is still missing.
By introducing the q-Schur algebras of type D and some fundamental multiplication formulas, we have made significant progress. In this talk, I will introduce the algebraic and geometric constructions of such q-Schur algebras, including their natural basis and fundamental multiplication formulas. If time permits, more applications such as the associated duality will be discussed.
This is joint work with Yiqiang Li and Zhaozhao Zhao.
In this talk, I will discuss latest development, which I call the Schur-Weyl-Hecke duality, initiated by Huanchen Bao and Weiqiang Wang in their study of quantum symmetric pairs and canonical basis theory. This duality connects the i-quantum groups U^j(n) and U^i(n) to the Hecke algebras of types B and C, respectively, and has many applications. However, in the type D case, such a duality, first attempted by Fan and Li, is still missing.
By introducing the q-Schur algebras of type D and some fundamental multiplication formulas, we have made significant progress. In this talk, I will introduce the algebraic and geometric constructions of such q-Schur algebras, including their natural basis and fundamental multiplication formulas. If time permits, more applications such as the associated duality will be discussed.
This is joint work with Yiqiang Li and Zhaozhao Zhao.
邀请人：吕仁才