Abstract
For all prime powers $q$ we restrict the unipotent characters of the special orthogonal groups $\text{SO}_{5}(q)$ and $\text{SO}_{7}(q)$ to a maximal parabolic subgroup. We determine all irreducible constituents of these restrictions for $\text{SO}_{5}(q)$ and a large part of the irreducible constituents for $\text{SO}_{7}(q)$.
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