Seminormal forms and Gram determinants for cellular algebras
Seminormal forms and Gram determinants for cellular algebras
复制标题
DOI：
10.1515/crelle.2008.042
复制
发表时间：
2006-04
期刊：
影响因子：
1.7
通讯作者：
Andrew Mathas;Marcos Soriano
中科院分区：
文献类型：
--
作者：
Andrew Mathas;Marcos Soriano
摘要本文提出了一种构造胞腔代数“正规型”的抽象框架。也就是说，给定一个胞腔R-代数A，它具有一个JM-元族，当JM-元分离A时，我们给出了构造A及其所有不可约表示的正交基的一般方法。在R的分式域上定义了A的正规型。重要的是，我们证明了每个不可约A-模的Gram行列式等于来自A的正规基的某些结构常数的乘积。在非分离的情况下，我们使用我们的正规化形式给出A的块分解的显式基。
Abstract This paper develops an abstract framework for constructing “seminormal forms” for cellular algebras. That is, given a cellular R-algebra A which is equipped with a family of JM-elements we give a general technique for constructing orthogonal bases for A, and for all of its irreducible representations, when the JM-elements separate A. The seminormal forms for A are defined over the field of fractions of R. Significantly, we show that the Gram determinant of each irreducible A-module is equal to a product of certain structure constants coming from the seminormal basis of A. In the non-separated case we use our seminormal forms to give an explicit basis for a block decomposition of A.