Hidden symmetric group actions

该项目是在代数拓扑，带来的想法，从等变同伦理论，连同代数和组合学有关的表示理论的对称群。它将研究拓扑学、代数学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的划分格的神经之间存在已知的等变同伦等价。分格上隐藏的额外作用将被显式化和研究。将探讨对称群的表示的结果。

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.