讲座题目Topic: Analyzing the p and q parts of character degrees of the symmetric group and related combinatorics

主办单位Organizer：三峡数学研究中心/Three Gorges Mathematical Research Center

报告专家Reporter: James Cossey, University of Akron

报告时间Date&Time (Chinese Time Zone)：2022.5.12, 9:00—11:00

报告地点Venue（线上Online）：Join Zoom Meeting

https://txstate.zoom.us/j/97791535907

Meeting ID: 977 9153 5907

专家简介 Brief Introduction of the Reporter：James (JP) Cossey is a Professor of Mathematics at the University of Akron. He received his PhD from the University of Wisconsin in 2005, under the direction of Martin Isaacs. Dr. Cossey researches topics in the representation theory of solvable groups and symmetric groups, as well as related combinatorics.

摘要Report Summary：The representation theory of the symmetric group is closely connected to the study of partitions. In particular, there is a bijection from the partitions of the positive integer n to the ordinary irreducible representations of the symmetric group S_n. The degree of the representation corresponding to the partition lambda is encoded in the hook lengths of lambda. We will start by looking at Anderson’s result from twenty years ago that began to relate the p-structure and the q-structure of these representations, where p and q are distinct primes. We will then discuss some very recent results that show that when the p-part of the character degree is as large as possible, then the q-part of the same character degree is in some sense very small. We will end with some related open questions.