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arXiv · 1608.06140

Restriction of irreducible modules for $\mbox{Spin}_{2n+1}(K)$ to $\mbox{Spin}_{2n}(K)$

Mikaël Cavallin
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Abstract

Let $K$ be an algebraically closed field of characteristic $p\geqslant 0$ and let $Y=\mbox{Spin}_{2n+1}(K)$ $(n\geqslant 3)$ be a simply connected simple algebraic group of type $B_n$ over $K.$ Also let $X$ be the subgroup of type $D_n,$ embedded in $Y$ in the usual way, as the derived subgroup of the stabilizer of a non-singular one-dimensional subspace of the natural module for $Y.$ In this paper, we give a complete set of isomorphism classes of finite-dimensional, irreducible, rational $KY$-modules on which $X$ acts with exactly two composition factors.

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BibTeXRIS

Mikaël Cavallin. 2016-08-22. Restriction of irreducible modules for $\mbox{Spin}_{2n+1}(K)$ to $\mbox{Spin}_{2n}(K)$. https://arxiv.org/abs/1608.06140

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