Hecke Algebras of TypeAwithq=−1
Hecke Algebras of TypeAwithq=−1
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A 型赫克代数，q=−1
DOI：
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发表时间：
1996
期刊：
影响因子：
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通讯作者：
Andrew Mathas
中科院分区：
文献类型：
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作者：
G. James;Andrew Mathas
本文研究特征为0的域上q =−1的A型Hecke代数的分解矩阵。本文给出了由1部或2部2-正则划分索引的分解矩阵的列的显式计算公式和由3部划分索引的分解矩阵的列的计算算法。结合这些结果，我们找到了分解矩阵的所有行，这些行由最多四个部分的分区索引。所有这些都是通过一个更一般的理论来实现的，该理论首先表明，由具有“巨大的2-核”的2-正则分区索引的分解矩阵的列中的分解数是Littlewood-Richardson系数。
Abstract In this paper we study the decomposition matrices of the Hecke algebras of type A with q =−1 over a field of characteristic 0. We give explicit formulae for the columns of the decomposition matrices indexed by all 2-regular partitions with 1 or 2 parts and an algorithm for calculating the columns of the decomposition matrix indexed by partitions with 3 parts. Combining these results we find all of the rows of the decomposition matrices which are indexed by partitions with at most four parts. All this is accomplished by means of a more general theory which begins by showing that the decomposition numbers in the columns of the decomposition matrices indexed by 2-regular partitions with “enormous 2-cores” are Littlewood–Richardson coefficients.