这是群论和图论方向的线上系列报告，我们希望能够促进国内外青年学者（博士生为主）在群论和图论研究上的交流。报告主题分布在（但不限于）以下研究方向：
This is a platform for young group theorists and graph theorists (mostly PhD students) to talk about their research and related topics online. The topic can be anything related to group theory and graph theory, including but not limited to the following.
一般地，系列报告定期于北京时间每周三下午16:00-17:00进行。
Our usual time is Wednesday 16:00-17:00 (GMT+8).
Title: Multiplicity-free induced characters of symmetric groups
Speaker: Pavel Turek (Royal Holloway, University of London)
Time: 16:00-17:00 (GMT+8), Wednesday May 14th
Location: Zoom: 262 780 8767 (passcode: gts2025)
Abstract:
Let \(n\) be a sufficiently large positive integer. A character is multiplicity-free if its irreducible constituents appear with multiplicity one. Wildon in 2009 and independently Godsil and Meagher in 2010 have found all multiplicity-free permutation characters of the symmetric group \(S_n\). In this talk, we focus on a significantly more general problem when the permutation characters are replaced by induced characters of the form \(\rho\!\uparrow^{S_n}\) with \(\rho\) irreducible.
Despite the nature of the problem, I explain, combining results from group theory, representation theory and combinatorics, why this problem may be feasible and present a close to full answer. I also mention some of my (often surprising) results to questions about conjugate partitions, which naturally arise when solving the problem, and the remarkable complete classification of subgroups \(G\) of \(S_n\), which have an irreducible character which stays multiplicity-free when induced to \(S_n\).
The seminar is currently based at the Southern University of Science and Technology (SUSTech, 南方科技大学).