Hidden symmetric group actions

隐藏的对称群动作

• 批准号: 2485500
• 金额: --
• 依托单位: University of Sheffield
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2020
• 资助国家: 英国
• 起止时间: 2020 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2485500
• 关键词: Hidden; symmetric; group; actions

The project is in algebraic topology, bringing in ideas from equivariant homotopy theory, together with algebra and combinatorics related to representation theory of the symmetric group. It will study some related situations in topology, algebra and combinatorics where the obvious action of the n-th symmetric group is in fact the restriction of a "hidden" action of the (n+1)-st symmetric group. This situation arises for spaces of trees and certain configuration spaces. There is a known equivariant homotopy equivalence between the n-th space of trees and the nerve of the lattice of partitions of n. The hidden extra action on the partition lattice will be made explicit and studied. Consequences for representations of the symmetric group will be explored.

该项目属于代数拓扑，引入了等变同伦理论的思想，以及与对称群表示论相关的代数和组合学。它将研究拓扑学、代数和组合学中的一些相关情况，其中第n个对称群的明显作用实际上是第(n+1)个对称群的“隐藏”作用的限制。这种情况出现在树空间和某些配置空间中。在树的第 n 个空间和 n 的分区格子的神经之间存在已知的等变同伦等价。划分格子上隐藏的额外作用将被明确并研究。将探讨对称群表示的后果。