### Abstract

We define a new class of quantum vertex algebras, based on the Hopf algebra H_{D} = [D] of "infinitesimal translations" generated by D. Besides the braiding map describing the obstruction to commutativity of products of vertex operators, H_{D}-quantum vertex algebras have as a main new ingredient a "translation map" that describes the obstruction of vertex operators to satisfying translation covariance. The translation map also appears as obstruction to the state-field correspondence being a homomorphism. We use a bicharacter construction of Borcherds to construct a large class of H_{D}-quantum vertex algebras. One particular example of this construction yields a quantum vertex algebra that contains the quantum vertex operators introduced by Jing in the theory of HallLittlewood polynomials.

Original language | English (US) |
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Pages (from-to) | 937-991 |

Number of pages | 55 |

Journal | Communications in Contemporary Mathematics |

Volume | 11 |

Issue number | 6 |

DOIs | |

State | Published - Dec 1 2009 |

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### Keywords

- Bicharacter
- Quantum vertex algebra

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

_{D}-quantum vertex algebras and bicharacters.

*Communications in Contemporary Mathematics*,

*11*(6), 937-991. https://doi.org/10.1142/S0219199709003624