Combinatorial constructions of modules for infinite-dimensional Lie algebras, I. Principal subspace
Combinatorial constructions of modules for infinite-dimensional Lie algebras, I. Principal subspace
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无限维李代数模的组合构造，I. 主子空间
DOI：
10.1016/0022-4049(95)00143-3
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发表时间：
1994
影响因子：
0.8
通讯作者：
Galin Georgiev
中科院分区：
文献类型：
--
作者：
Galin Georgiev
这是一系列研究仿射李代数的组合(不含减法)基和标准模的特征，以及这些模的各个子空间和陪集空间的系列文章的第一篇。在第一部分中，我们考虑了仿射李代数g-̂，g：=sl(n+1，C)，n-≥-1在任意正整数级k的某些标准模，并构造了它们的主子空间的基(最近由Feigin和Stoyanovsky(1994年)引入和研究)。根据划分给出基：将颜色i，1≤i≤n和电荷S，1≤S≤k分配给划分的每个部分，使得相同颜色和电荷的部分满足一定的差异条件。这些部分表示顶点算符的“傅立叶系数”，可以解释为享受与g的Cartan矩阵有关的(两粒子)统计相互作用的“准粒子”。在真空模的特殊情况下，与我们的基有关的特征标公式是Feigin和Stoyanovsky(1994)中宣布的公式。给出了第一级标准真空ĝ-模的新组合特征。
This is the first of a series of papers studying combinatorial (with no “subtractions”) bases and characters of standard modules for affine Lie algebras, as well as various subspaces and “coset spaces” of these modules. In part I we consider certain standard modules for the affine Lie algebra g ̂ , g: = sl(n + 1, C ) , n ≥ 1, at any positive integral level k and construct bases for their principal subspaces (introduced and studied recently by Feigin and Stoyanovsky (1994)). The bases are given in terms of partitions: a color i, 1 ≤ i ≤ n, and a charge s, 1 ≤ s ≤ k, are assigned to each part of a partition, so that the parts of the same color and charge comply with certain difference conditions. The parts represent “Fourier coefficients” of vertex operators and can be interpreted as “quasi-particles” enjoying (two-particle) statistical interaction related to the Cartan matrix of g. In the particular case of vacuum modules, the character formula associated with our basis is the one announced in Feigin and Stoyanovsky (1994). New combinatorial characters are proposed for the whole standard vacuum ĝ-modules at level one.
影响因子：
2.8
作者：
BELAVIN, AA;POLYAKOV, AM;ZAMOLODCHIKOV, AB
通讯作者：
ZAMOLODCHIKOV, AB