$H_D$-Quantum Vertex Algebras and Bicharacters
$H_D$-Quantum Vertex Algebras and Bicharacters
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DOI：
10.1142/s0219199709003624
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发表时间：
2007-06
期刊：
影响因子：
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通讯作者：
I. Anguelova;M. Bergvelt
中科院分区：
文献类型：
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作者：
I. Anguelova;M. Bergvelt
基于由D生成的“无穷小平移”的Hopf代数H_D=\mathbb{C}[D]，定义了一类新的量子顶点代数.除了描述顶点算子的乘积对交换性的阻碍的辫子映射外，$H_D$-量子顶点代数还增加了一个描述顶点算子对满足平移协方差的阻碍的“平移映射”.平移映射也表现为态场对应是同态的障碍。利用Borcherds的双特征标构造方法构造了一大类$H_D$-量子顶点代数.这种构造的一个特殊例子产生了一个量子顶点代数，它包含了Jing在霍尔-利特尔伍德多项式理论中引入的量子顶点算子。
We define a new class of quantum vertex algebras, based on the Hopf algebra $H_D=\mathbb{C}[D]$ 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 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 Hall-Littlewood polynomials.