Identities for cylindric Schur functions

：Christian Krattenthaler（奥地利维也纳大学）
：2023-04-06 15:00
：腾讯会议ID：794-175-547（无密码）

报告人：Christian Krattenthaler（奥地利维也纳大学）

时  间：2023年4月6日下午15:00-16:30

地  点：腾讯会议ID：794-175-547（无密码）

内容摘要:

I shall tell the story of a very small seed (a specific enumeration problem) that in the end gives rise to an unexpected general result (in the theory of symmetric functions) that at first sight does not seem to have anything to do with the original problem.

The original problem is about finding a bijection between two specific sets of lattice paths. After reformulation, this problem leads us in the end to discover a far-reaching generalization of a classical one, but difficult-to-prove result in the theory of symmetric functions due to Basil Gordon, as realized by Edward Bender and Donald Knuth. The latter result provides a determinantal formula for a specific sum of Schur functions that plays an important role in other contexts, most notably in the enumeration of plane partitions and in the representation theory of classical groups.

In my talk I shall explain all the above terms and connections, and describe the above sketched path of discovery of an unexpected new result, while the original problem of finding a bijection was left unsolved.

This is joint work with JiSum Huh, Jang Soo Kim and Soichi Okada.

个人简介：

Christian Krattenthaler, 奥地利维也纳大学数学学院教授，主要从事代数组合和数论方向的研究，在众多知名的数学杂志上发表了文章，包括AiM, CMP, DMJ, JCTA, MAMS, PNAS, TAMS。曾获得过奥地利数学协会Förderungspreis奖励, 奥地利国家基金委Wittgenstein奖金(这是奥地利授予科研工作者的最高奖项)，2011年被评为欧洲科学院(Academia Europaea)院士。

 

联系人：靳宇