English

Some translations in the second lowest two-sided cell of an affine Weyl group

Representation Theory 2020-12-25 v1

Abstract

We are interested in cell properties of translations in affine Weyl groups. We find out some translations in the second lowest two-sided cell of an affine Weyl group and use the translations to formulate a refinement of Jianyi Shi's conjecture on the number of left cells in the second lowest two-sided cell. We verify the refinement for an affine Weyl group of type A~n1\tilde A_{n-1} and type G~2\tilde G_2.

Keywords

Cite

@article{arxiv.2012.13221,
  title  = {Some translations in the second lowest two-sided cell of an affine Weyl group},
  author = {Yannan Qiu},
  journal= {arXiv preprint arXiv:2012.13221},
  year   = {2020}
}