Lakshmibai–Seshadri Paths Fixed by a Diagram Automorphism

We prove that the Lakshmibai–Seshadri paths fixed by a diagram automorphism ω of a Kac–Moody algebra can be identified with the Lakshmibai–Seshadri paths for the orbit Lie algebra, by introducing ω-root operators. We also give certain formulas for the twining characters of integrable highest weight modules over a symmetrizable Kac–Moody algebra and of Demazure modules for a finite-dimensional semi-simple Lie algebra.