2025/06/02 by Terwilliger, Paul
#05E30 #Combinatorics (math.CO) #FOS: Mathematics #Quantum Algebra (math.QA)
paper · doi:10.48550/arxiv.2506.02190
We consider a 2-homogeneous bipartite distance-regular graph Γ with diameter D ≥ 3. We assume that Γ is not a hypercube nor a cycle. We fix a Q-polynomial ordering of the primitive idempotents of Γ. This Q-polynomial ordering is described using a nonzero parameter q ∈ \mathbb C that is not a root of unity. We investigate Γ using an S3-symmetric approach. In this approach one considers V⊗ 3 = V ⊗ V ⊗ V where V is the standard module of Γ. We construct a subspace Λ of V⊗ 3 that has dimension \binomD+33, together with six linear maps from Λ to Λ. Using these maps we turn Λ into an irreducible module for the nonstandard quantum group U^′q(\mathfrakso6) introduced by Gavrilik and Klimyk in 1991.