学术报告

走向现代数学学术报告 - 崔沛仪博士(No. 508)

报告题目:A decomposition of the category of modulo l representations of SL_n(F)

报告人:崔沛仪 博士(维也纳大学)

报告时间:2022年5月6日周五,下午16:00

报告地点:腾讯会议 911 493 212

报告摘要:Let F be a p-adic field, and k an algebraically closed field of characteristic l different from p. In this talk, we will first give a category decomposition of Rep_k(SL_n(F)), the category of smooth k-representations of SL_n(F), with respect to the GL_n(F)-equivalent supercuspidal classes of SL_n(F), which is not always a block decomposition in general. We then give a block decomposition of the supercuspidal subcategory Rep_k(SL_n(F))_{SC}, by introducing a partition on each GL_n(F)-equivalent supercuspidal class by type theory, which gives a prediction of the block decomposition of Rep_k(SL_n(F)). We give an example where a block of Rep_k(SL_2(F)) is defined with several SL_2(F)-equivalent supercuspidal classes, which is different from the case where I is zero. We end this talk by giving a prediction on the block decomposition of Rep_k(A) for a general p-adic group A.

报告人简介:崔沛仪,2019年博士毕业于法国巴黎六大,目前于奥地利维也纳大学任博士后。主要研究包括p-进群的表示与局部Langlands对应。