Standard paths and standard monomials fixed by a diagram automorphism
Let \(\mathfrak{g}\) be a Kac-Moody algebra with symmetrizable generalized Cartan matrix (GCM) and \(\omega\) an automorphism of \(\mathfrak{g}\) induced by a Dynkin diagram automorphism. To such a \(\mathfrak{g}\) and \(\omega\) there can be associated another Kac-Moody algebra denoted \(\breve{\mathfrak{g}}\) and called the orbit Lie algebra of \(\mathfrak{g}\). The paper shows that the standard paths and the standard monomials fixed by a diagram automorphism of \(\mathfrak{g}\) can be identified with the standard paths and the standard monomials for \(\breve{\mathfrak{g}}\). This enables the authors to give a combinatorial proof of twining character formulas for an integrable highest weight module and for a Demazure module.
scientific article; zbMATH DE number 1797483
scientific article