mirabolic Hecke algebras, Schur-Weyl duality and Frobenius character formulas

报告主题：mirabolic Hecke algebras, Schur-Weyl duality and Frobenius character formulas
报告时间：2026-05-17 08:30
报告地点：1C207
专家姓名：万金奎
专家简介：万金奎，深圳大学数学科学学院教授，国家级青年人才，博士毕业于美国弗吉尼亚大学，曾访问澳大利亚新南威尔士大学、美国弗吉尼亚大学等。
报告内容：We first give a new presentation for mirabolic Hecke algebras $MH_n(q)$ over $\mathbb{C}(q)$ and derive an alternative basis. Building on this, we construct a basis for the cocenter of $MH_n(q)$, which allows us to define the character table for $MH_n(q)$. We then establish the Schur-Weyl duality for these algebras. As an application, we obtain the Frobenius character formula, in the ring of symmetric functions, for the irreducible characters of $MH_n(q)$. We then derive a recursive Murnaghan-Nakayama rule for calculating the character table.