Crystal structure on the set of Lakshmibai-Seshadri paths of an arbitrary level-zero shape
Crystal structure on the set of Lakshmibai-Seshadri paths of an arbitrary level-zero shape
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任意零级形状的 Lakshmibai-Seshadri 路径集上的晶体结构
DOI：
10.1112/plms/pdm034
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发表时间：
2008
期刊：
影响因子：
--
通讯作者：
S. Naito and D. Sagaki
中科院分区：
文献类型：
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作者：
Matsui M;et al;石田佐恵子;小西恵美子;S. Naito and D. Sagaki
设λ=∑i∈I0 miϖi, mi∈0∈I0，是一个仿射李代数ℊ在π上的零级主导积分权，其中ϖi，i∈I0，是零级基本权，并且letB（λ）是形状λ的所有Lakshmibai-Seshadri路径的晶体。首先，我们给出了晶体b （λ）分解成连通分量的显式描述，并表明所有连通分量都是两两“同构”的（直到权值的偏移）。其次，我们“实现”了包含直线πλ的b （λ）的连接分量b0 （λ）作为晶体（带权重晶格，其中δ为ℊ的零根）的亲射化（带权重晶格ep）的指定子晶体（我们在之前的论文中研究过）。数学。Res. no .2005(2005) 815-840)。
Let λ=∑i∈I0miϖi, withmi∈ℤ⩾0fori∈I0, be a level‐zero dominant integral weight for an affine Lie algebra ℊ over ℚ, where the ϖi,i∈I0, are the level‐zero fundamental weights, and letB(λ) be the crystal of all Lakshmibai–Seshadri paths of shape λ. First, we give an explicit description of the decomposition of the crystalB(λ) into connected components and show that all the connected components are pairwise ‘isomorphic’ (up to a shift of weights). Second, we ‘realize’ the connected componentB0(λ) ofB(λ) containing the straight line πλas a specified subcrystal of the affinization(with weight latticeP) of the crystal(with weight lattice, where δ is the null root of ℊ ), which we studied in a previous paper (Int. Math. Res. Not.2005 (2005) 815–840).