Geometric representations of finite groups on real toric spaces

Soojin Cho, Suyoung Choi, Shizuo Kaji

Research output: Contribution to journalArticlepeer-review

Abstract

We develop a framework to construct geometric representations of finite groups G through the correspondence between real toric spaces XR and simplicial complexes with characteristic matrices. We give a combinatorial description of the G-module structure of the homology of XR. As applications, we make explicit computations of the Weyl group representations on the homology of real toric varieties associated to the Weyl chambers of type A and B, which show an interesting connection to the topology of posets. We also realize a certain kind of Foulkes representation geometrically as the homology of real toric varieties.

Original languageEnglish
Pages (from-to)1265-1283
Number of pages19
JournalJournal of the Korean Mathematical Society
Volume56
Issue number5
DOIs
Publication statusPublished - 2019

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Fingerprint Dive into the research topics of 'Geometric representations of finite groups on real toric spaces'. Together they form a unique fingerprint.

Cite this