The particle system labeled the asymmetric simple exclusion process (ASEP) involves two classes of particles. A generator of ASEP can be produced from both a probabilistic construction and an algebraic construction, which result in the same generator for Type-A Lie algebras. However, specifying to Type-D ASEP, the methods do not produce the same generator when considering the Type D so(6)-model; in fact, the algebraic method constructs a generator allowing for more states than are possible in the typical Type D-ASEP. We test whether the same conclusion holds for the so(8)-model by decomposing and analyzing various  so(8)-modules in order to construct a fused Type D ASEP generator from a central element of  U_q(so(8)). We conclude that neither the original statement nor this more flexible statement can hold for such a generator.

Speaker: Lillian Stolberg, University of Rochester