The existence of non-abelian local constants and their properties
In his Ph.D thesis, John Tate attached local constants with characters of a non-Archimedean local field of characteristic zero. Robert Langlands proved the existence theorem of non-abelian local constants of higher dimensional complex local Galois representations. Later Helmut Koch summarized Langlands' strategy and gave shorter version (group theoretic) of Langlands' proof. The Brauer induction formula plays a very crucial role in the Langlands' proof. Robert Boltje gives a canonical version of the Brauer induction formula. In this paper, we review the Langlands' strategy via Boltje's canonical Brauer induction formula. After that we also review properties of local constants, some applications and open problems.