An Explicit Description of the B(\infty) Crystal For Generalized Quantum Groups of a Family of Comet Quivers

Abstract

Tristan Bozec gave a definition of generalized quantum groups that extends the usual definition of quantum groups to finite quivers with loops at vertices, and he introduced a theory of generalized crystals for this new family of Hopf algebras. We explicitly characterize the generalized crystal $\mathcal{B}(\infty )$ associated to a certain family of quivers with multiple loops by providing a complete set of relations among the Kashiwara operators themselves.

13 pages

References in corpus (1)

• Quivers with loops and perverse sheaves