  This paper deals with the study of the two-dimensional Dirac operatorwith
infinite mass boundary condition in a sector. We investigate the question
ofself-adjointness depending on the aperture of the sector: when the sector is
convexit is self-adjoint on a usual Sobolev space whereas when the sector is
non-convexit has a family of self-adjoint extensions parametrized by a complex
number of theunit circle. As a byproduct of this analysis we are able to give
self-adjointnessresults on polygones. We also discuss the question of
distinguished self-adjointextensions and study basic spectral properties of the
operator in the sector.
