Title: A unitary "quantization commutes with reduction" map for the adjoint action of a compact Lie group,
Abstract: Let $K$ be a simply connected compact Lie group and $T^{\ast}(K)$ its
cotangent bundle. We consider the problem of "quantization commutes with
reduction" for the adjoint action of $K$ on $T^{\ast}(K).$ We quantize both
$T^{\ast}(K)$ and the reduced phase space using geometric quantization with
half-forms. We then construct a geometrically natural map from the space of
invariant elements in the quantization of $T^{\ast}(K)$ to the quantization of
the reduced phase space. We show that this map is a constant multiple of a
unitary map.