New infinite hierarchies of polynomial identities related to the Capparelli partition theorems

We prove a new polynomial refinement of the Capparelli's identities. Using a special case of Bailey's lemma we prove many infinite families of sum-product identities that root from our finite analogues of Capparelli's identities. We also discuss the q ↦ 1 / q duality transformation of...
Ausführliche Beschreibung

We prove a new polynomial refinement of the Capparelli's identities. Using a special case of Bailey's lemma we prove many infinite families of sum-product identities that root from our finite analogues of Capparelli's identities. We also discuss the q ↦ 1 / q duality transformation of the base identities and some related partition theoretic relations. Ausführliche Beschreibung