Congruence for Lattice Path Models with Filter Restrictions and Long Steps

Abstract

We derive a path counting formula for a two-dimensional lattice path model with filter restrictions in the presence of long steps, source and target points of which are situated near the filters. This solves the problem of finding an explicit formula for multiplicities of modules in tensor product decomposition of T(1)⊗N for Uq(sl2) with divided powers, where q is a root of unity. Combinatorial treatment of this problem calls for the definition of congruence of regions in lattice path models, properties of which are explored in this paper.

Keywords

• lattice path models
• enumerative combinatorics
• quantum groups at roots of unity
• tensor product decomposition