Factorial characters of the classical Lie groups
Factorial characters of the classical Lie groups
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经典李群的阶乘特征
DOI：
10.1016/j.ejc.2018.01.011
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发表时间：
2018
期刊：
影响因子：
--
通讯作者：
R. King
中科院分区：
文献类型：
--
作者：
Angèle M. Foley;R. King
正如阶乘Schur函数的定义作为一个比率的决定因素允许一个人来表明，他们满足Jacobi-Trudi型恒等式，并有一个明确的组合实现方面的半标准tableaux，所以我们在这里提供的阶乘不可约字符的经典李群的定义作为比率的决定因素，共享这两个功能。这些阶乘特征标各自由一个划分λ=（λ 1，λ 2，...，λ n）指定，并且在每种情况下都导出一个带标记的Jacobi-Trudi恒等式，该恒等式将阶乘特征标表示为由一部分划分（m）指定的相应阶乘特征标的行列式，我们提供了生成函数。这些恒等式是通过使用从这些生成函数导出的某些递归关系来操纵行列式而建立的。的阶乘字符在tableaux的组合实现的过渡，然后建立通过不相交的格子路径模型。结果适用于gl（n），so（2n + 1），sp（2n）和o（2n），并利用新定义的阶乘差特征标推广到so（2n）的情形.
Just as the definition of factorial Schur functions as a ratio of determinants allows one to show that they satisfy a Jacobi–Trudi-type identity and have an explicit combinatorial realisation in terms of semistandard tableaux, so we offer here definitions of factorial irreducible characters of the classical Lie groups as ratios of determinants that share these two features. These factorial characters are each specified by a partition, λ=(λ 1, λ 2,…, λ n), and in each case a flagged Jacobi–Trudi identity is derived that expresses the factorial character as a determinant of corresponding factorial characters specified by one-part partitions,(m), for which we supply generating functions. These identities are established by manipulating determinants through the use of certain recurrence relations derived from these generating functions. The transitions to combinatorial realisations of the factorial characters in terms of tableaux are then established by means of non-intersecting lattice path models. The results apply to g l (n), s o (2 n+ 1), s p (2 n) and o (2 n), and are extended to the case of s o (2 n) by making use of newly defined factorial difference characters.