Combinatorics of vertex operators and deformed W-algebra of type D(2,1;alpha)
Combinatorics of vertex operators and deformed W-algebra of type D(2,1;alpha)
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顶点算子的组合和 D(2,1;alpha) 类型的变形 W 代数
DOI：
10.1016/j.aim.2022.108331
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发表时间：
2022
期刊：
影响因子：
--
通讯作者：
and E.Mukhin
中科院分区：
文献类型：
--
作者：
B.Feigin;M.Jimbo;and E.Mukhin
我们考虑具有费米子屏蔽电流的屏蔽算子集。我们研究了形式上与屏蔽算子可交换的顶点算子和，假设每个顶点算子与所有仅具有简单极点的屏蔽电流都有有理压缩。我们发展和使用了QQ字符的方法，它是用变形Cartan矩阵描述的组合对象。我们证明了每个QQ字符产生一个与筛选算子交换的顶点算子之和，并在其无穷大的情况下描述了理解这个和的方法。我们讨论了QQ-特征标的组合以及它们与量子群表示的Q-特征标的关系。我们提供了一些明确的QQ字符的例子，重点是D(2，1；α)的情况。我们描述了这些例子与各种运动积分的关系。
We consider sets of screening operators with fermionic screening currents. We study sums of vertex operators which formally commute with the screening operators assuming that each vertex operator has rational contractions with all screening currents with only simple poles. We develop and use the method of qq-characters which are combinatorial objects described in terms of deformed Cartan matrix. We show that each qq-character gives rise to a sum of vertex operators commuting with screening operators and describe ways to understand the sum in the case it is infinite. We discuss combinatorics of the qq-characters and their relation to the q-characters of representations of quantum groups. We provide a number of explicit examples of the qq-characters with the emphasis on the case of D (2, 1; α). We describe a relationship of the examples to various integrals of motion.