Abstract
In Theorem 1 we classify all finite-dimensional indecomposable representations of the infinite dihedral group over an arbitrary field k of char k ≠ 2. Of course, that result is equivalent to the problem of finding a “normal form” for a pair of involutions in GL n ( k). In Theorem 2 we find necessary and sufficient conditions for a pair of conjugate involutions in GL n ( k) to be conjugate via an involution, where k is assumed to be algebraically closed and char k ≠ 2.
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