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

Uma Roy; Seth Shelley-Abrahamson

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arXiv · 1510.03086

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

Uma Roy·Seth Shelley-Abrahamson

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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.

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Uma Roy, Seth Shelley-Abrahamson. 2015-10-11. An Explicit Description of the B(\infty) Crystal For Generalized Quantum Groups of a Family of Comet Quivers. https://arxiv.org/abs/1510.03086

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