# Structure of certain Weyl modules for the Spin groups

## TL;DR

This paper determines the structure and dimensions of specific Weyl modules for Spin groups over algebraically closed fields of characteristic not equal to 2, and analyzes restrictions of SL modules to SO groups.

## Contribution

It provides the explicit structure of certain Weyl modules for Spin groups and the composition factors of restricted SL modules, advancing understanding of their representation theory.

## Key findings

- Structure of Weyl modules for Spin groups in characteristic p≠2
- Dimensions of irreducible modules for Spin groups
- Decomposition of restricted SL modules to SO groups

## 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 $\mbox{SO}(W).$