Title: Leading terms of relations on a level 5 module over the twisted affine Lie algebra of rank 1

Abstract: Two Capparelli’s identities are the first new combinatorial identities coming from the representation theory of the twisted affine Lie algebra of rank 1 at level 3. Later the Meurman-Primc identities were discovered for all standard modules of the untwisted affine Lie algebra of rank 1 and it was noticed that those for two level 1 modules coincide with Capparelli’s identities. By using Lepowsky’s and Wakimoto’s product formulas for specialized characters of standard modules, Julius Borcea established a 1-1 correspondence for product formulas of level k modules for the untwisted affine Lie algebra of rank 1 and level 2k+1 modules for the twisted affine Lie algebra of rank 1, and this raised the question whether the corresponding combinatorial identities coincide for all natural numbers k. In a joint work with Stefano Capparelli and Arne Meurman we construct a list of leading terms of relations for level 5 module over the twisted affine Lie algebra of rank 1 and show that the corresponding combinatorial identity drastically differs from the one for Borcea’s dual. Although the list of leading terms is incomplete, the obtained results shed new light on expected combinatorial identities and give rise to new questions for research.