Quantized W-algebra of sl(2,1) : a construction from the quantization of screening operators
Quantized W-algebra of sl(2,1) : a construction from the quantization of screening operators
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sl(2,1) 的量化 W 代数：筛选算子量化的构造
DOI：
10.1090/conm/248/03819
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发表时间：
1998
期刊：
影响因子：
--
通讯作者：
B. Feigin
中科院分区：
文献类型：
--
作者：
Jintai Ding;B. Feigin
本文从玻色化出发，研究了自由场量子化屏算符与任意量子化屏算符交换或交换到全差的算符。证明了如果存在一个两顶点算子之和形式的算子，它与量子化屏蔽算子具有最简单的相关函数，即一个极点和一个零点的函数，则屏蔽算子和这个算子是唯一确定的，并且这个算子是量子化Virasoro代数.对于屏蔽体为费米子的情形，存在一族这类算符，它们给出了新的代数结构。类似地，我们研究了两个量子屏蔽算子的情况，对于一般情况，它唯一地给出了对应于$sl（3）$的量子W-代数，对于两个屏蔽算子之一或两者都是费米子的情况，我们给出了一个新的代数，它是对应于${\frak sl}（2，1）$的量子W-代数。
Starting from bosonization, we study the operator that commute or commute up-to a total difference with of any quantized screen operator of a free field. We show that if there exists a operator in the form of a sum of two vertex operators which has the simplest correlation functions with the quantized screen operator, namely a function with one pole and one zero, then, the screen operator and this operator are uniquely determined, and this operator is the quantized virasoro algebra. For the case when the screen is a fermion, there are a family of this kind of operator, which give new algebraic structures. Similarly we study the case of two quantized screen operator, which uniquely gives us the quantized W-algebra corresponding to $sl(3)$ for the generic case, and a new algebra, which is a quantized W-algebra corresponding to ${\frak sl}(2,1)$, for the case that one of the two screening operators is or both are fermions.