University/Organization
Mathematics Department
University of Wisconsin – Whitewater
Whitewater, Wisconsin
Mathematics Department
University of Wisconsin – Whitewater
Whitewater, Wisconsin
Title
On the Coxeter Cohomology of Irreducible Representations of Symmetric Groups
Synopsis
This work is part of a research program to compute the Hochschild homology groups of specific quotients of polynomial rings via Coxeter cohomology, which utilizes an isomorphism provided by Larsen and Lindenstrauss. While previous work has focused exclusively on the two-variable case, we extend some results to all values of d. Notably, we show that when the tensor representation is replaced by an irreducible representation, the Eu-ler characteristic of the corresponding Coxeter cohomology is given by a polynomial with bounded degree. Although the problem is motivated by algebra and topology, the solution relies primarily on combinatorial arguments.