Cyclic symmetry classes
Cyclic symmetry classes
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循环对称类
DOI：
10.1016/0021-8693(76)90204-0
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发表时间：
1976
期刊：
影响因子：
--
通讯作者：
L. Cummings
中科院分区：
文献类型：
--
作者：
L. Cummings
我们讨论的是[5]中定义的张量的对称类。贯穿V是一个n维复向量空间，V是Z '上m个逆变张量的空间。如果... e，是V的任何基，则V具有基es= e，s（，）0. 0 es（m）（'1其中s在r上运行，.，，从（1，...，n}。因此V具有维数nnr。设G是S，的子群，{I，.，m}。G的一个线性特征标是群同态X：G-@*，其中@* 是非零复数的乘法群。Q 'e表示相应的对称类VXm（G）。对称算子5 '的值域为0”V-0”I/是V？(G)其中，P（r）：@）”V-0”V是由下式定义的线性映射：
We are concerned with symmetry classes of tensors as defined in [5]. Throughout V is an n-dimensional complex vector space and@“V is the space of m contravariant tensors over Z’. If e,,..., e, is any basis of V then@“V has the basis es= e, s (,) 0... 0 es (m)(‘1 where s runs over r,,.,, the set of all sequences of length m chosen from (l,..., n}. Thus@““V has dimension nnr. Let G be a subgroup of S,,,, the group of all permutations of {I,..., m}. A linear character of G is a group homomorphism X: G-@* where@* is the multiplicative group of nonzero complex numbers. Q’e denote the corresponding symmetry class by VXm (G). The range of a symmetry operator 5’: 0” V-0” I/is a model of V?(G) where P (r):@)” V-0” V is the linear mapping defined by