Standard Paths and Standard Monomials Fixed by a Diagram Automorphism

We show that the standard paths and the standard monomials fixed by a diagram automorphism for a Kac–Moody algebra can be identified with the standard paths and the standard monomials for the orbit Lie algebra of , respectively. By using these results, we give a combinatorial proof of twining character formulas for an integrable highest weight module and for a Demazure module within the framework of path models.