A geometrization of Zelevinsky's derivatives
数学专题报告
报告题目(Title)：A geometrization of Zelevinsky's derivatives
报告人(Speaker)：邓太旺（北京雁栖湖应用数学研究院）
地点(Place)：后主楼1220报告厅
时间(Time)：2024年6月25日 16:00-16:50
邀请人(Inviter)：肖杰、覃帆、周宇、方杰鹏、兰亦心
报告摘要
In the 1970s, Bernstein and Zelevinsky introduced a set of operators that act on the Grothendieck group of the category of admissible representations for $GL_n(Q_p)$. These operators play a crucial role in their classification of irreducible representations of $GL_n$. Later, Zelevinsky's derivatives, also known as Bernstein-Zelevinsky operators, found several important applications in automorphic theory. However, determining the Zelevinsky derivative of an irreducible representation is generally challenging. In this talk, we provide an interpretation of Zelevinsky's derivatives as dual to Lusztig's geometric inductions. As a byproduct, we derive a multiplicity formula for computing Zelevinsky's derivatives.
