Combinatorial constructions of modules for infinite-dimensional Lie algebras, II. Parafermionic space
Combinatorial constructions of modules for infinite-dimensional Lie algebras, II. Parafermionic space
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无限维李代数模的组合构造，II。
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发表时间：
1995
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通讯作者：
Galin Georgiev
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作者：
Galin Georgiev
仿射李代数$\ga$的标准模具有称为仿费米子空间的自然子模-与$\ga $相关的所谓仿费米子共形场论的基本空间。
我们研究了$\ga = \widehat{sl}（n+1，\C）$对任意正整数水平$k \geq 2.$推广了Lepowsky，Wilson和Primc的Z$-代数方法，构造了仿费米子空间的组合基.这些分区的一部分代表广义顶点算子（仿费米子流）的“傅立叶系数”，可以解释为统计相互作用的准粒子，颜色为i，1 leq i leq n，$，电荷为s，1 leq s leq k-1。从组合的观点来看，这些基与作者在[GeI]中构造的水平$k-1$主子空间的基本质上是相同的。在真空模的特殊情况下，与我们的基相关联的字符（字符串函数）是Kuniba，Nakanishi和Suzuki [KNS]在Bethe Anglands布局中的公式。
对全标准真空$\ga$-模建立了新的组合特征标。
The standard modules for an affine Lie algebra $\ga$ have natural subquotients called parafermionic spaces -- the underlying spaces for the so-called parafermionic conformal field theories associated with $\ga.$
We study the case $\ga = \widehat{sl}(n+1,\C)$ for any positive integral level $k \geq 2.$ Generalizing the $\cal Z$-algebra approach of Lepowsky, Wilson and Primc, we construct a combinatorial basis for the parafermionic spaces in terms of colored partitions. The parts of these partitions represent ''Fourier coefficients'' of generalized vertex operators (parafermionic currents) and can be interpreted as statistically interacting quasi-particles of color $i,\;1\leq i \leq n,$ and charge $s,\; 1\leq s \leq k-1.$ From a combinatorial point of view, these bases are essentially identical with the bases for level $k-1$ principal subspaces constructed by the author in [GeI]. In the particular case of the vacuum module, the character (string function) associated with our basis is the formula of Kuniba, Nakanishi and Suzuki [KNS] conjectured in a Bethe Ansatz layout.
New combinatorial characters are established for the whole standard vacuum $\ga$-modules.