Representations of anisotropic unitary groups

Abstract:

Let $SU(f)$ be the special unitary group of an anisotropic hermitian form $f$ over a field $k$. Assume $f$ represents only one norm class in $k$. The representations $\alpha : SU(f) \to SL(n, R)$ are characterized when $R$ is a commutative ring with $2$ not a zero divisor and $n = \dim f \geqslant 3$ with $n \ne 4, 6$. In particular, a partial classification of the normal subgroups of $SU(f)$ is given when $k$ is the function field ${\mathbf {C}}(X)$.