Structure of certain Weyl modules for the Spin groups

Mikaël Cavallin

Structure of certain Weyl modules for the Spin groups

Representation Theory 2017-05-12 v2

Authors: Mikaël Cavallin

Abstract

Let $K$ be an algebraically closed field of characteristic $p\geqslant 0$ and let $W$ be a finite-dimensional $K$ -space of dimension greater than or equal to $5.$ In this paper, we give the structure of certain Weyl modules for $G=\mbox{Spin}(W)$ in the case where $p\neq 2,$ as well as the dimension of the corresponding irreducible, finite-dimensional, rational $KG$ -modules. In addition, we determine the composition factors of the restriction of certain irreducible, finite-dimensional, rational $K\mbox{SL}(W)$ -modules to $\mbox{SO}(W).$

Keywords

weyl groups and algebras weyl group representations module theory

Cite

@article{arxiv.1704.01803,
  title  = {Structure of certain Weyl modules for the Spin groups},
  author = {Mikaël Cavallin},
  journal= {arXiv preprint arXiv:1704.01803},
  year   = {2017}
}

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