  We derive analytic formulas for the zero-modes of the Dirac equation in the
adjoint representation in the background field of Q=1 SU(N) calorons. Solutions
with various boundary conditions are obtained, including the physically most
relevant cases of periodic and antiperiodic ones. The latter are essential
ingredients in a semiclassical treatment of finite temperature supersymmetric
Yang-Mills theory. A detailed discussion of adjoint zero-modes in several other
contexts is also presented.
