Factorization of the canonical bases for higher-level Fock spaces
Factorization of the canonical bases for higher-level Fock spaces
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DOI：
10.1017/s0013091510000519
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发表时间：
2009-09
影响因子：
0.7
通讯作者：
S. Ariki;N. Jacon;C. Lecouvey
中科院分区：
文献类型：
--
作者：
S. Ariki;N. Jacon;C. Lecouvey
摘要 l 级 Fock 空间允许规范基 $\mathcal{G}_{e}$ 和 $\smash{\mathcal{G}_{\infty}}$。它们对应于 $\smash{\mathcal{U}_{v}(\widehat{\mathfrak{sl}}_{e})}$ 和 $\mathcal{U}_{v}({\mathfrak{sl}}_{\infty})$ 模块结构。我们确定与这两个基相关的转移矩阵是单位三角形，系数为 ℕ[v]。对空 l 分区生成的最高权重模块的限制给出了 Geck 和 Rouquier 关于与 Ariki-Koike 代数相关的分解矩阵分解的定理的自然量化。
Abstract The level l Fock space admits canonical bases $\mathcal{G}_{e}$ and $\smash{\mathcal{G}_{\infty}}$. They correspond to $\smash{\mathcal{U}_{v}(\widehat{\mathfrak{sl}}_{e})}$ and $\mathcal{U}_{v}({\mathfrak{sl}}_{\infty})$-module structures. We establish that the transition matrices relating these two bases are unitriangular with coefficients in ℕ[v]. Restriction to the highest-weight modules generated by the empty l-partition then gives a natural quantization of a theorem by Geck and Rouquier on the factorization of decomposition matrices which are associated to Ariki–Koike algebras.