The block decomposition of finite-dimensional representations of twisted loop algebras
The block decomposition of finite-dimensional representations of twisted loop algebras
复制标题
扭曲环代数有限维表示的分块分解
DOI：
10.2140/pjm.2010.244.335
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发表时间：
2008
期刊：
影响因子：
--
通讯作者：
Prasad Senesi
中科院分区：
文献类型：
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作者：
Prasad Senesi
设L σ (g)为具有非平凡图自同构σ的简单复李代数g的扭环代数。虽然L σ (g)的有限维表示的范畴_ σ不是半简单的，但它可以写成不可分解的子范畴（范畴的块）的和。为了描述这些和，我们引入了L σ (g)的扭曲谱特征。这些是Chari和Moura为非扭转环代数L(g)定义的谱特征的某些等价类，它们被用来描述L(g)的有限维表示的块。在此，我们采用这种分解方法，利用扭曲谱特征来参数化和描述函数的频谱块。
Let L σ (g) be the twisted loop algebra of a simple complex Lie algebra g with nontrivial diagram automorphism σ. Although the category ℱ σ of finite-dimensional representations of L σ (g) is not semisimple, it can be written as a sum of indecomposable subcategories (the blocks of the category). To describe these summands, we introduce the twisted spectral characters for L σ (g). These are certain equivalence classes of the spectral characters defined by Chari and Moura for an untwisted loop algebra L(g), which were used to provide a description of the blocks of finite-dimensional representations of L (g). Here we adapt this decomposition to parametrize and describe the blocks of ℱ σ via the twisted spectral characters.