Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9498230 | Linear Algebra and its Applications | 2005 | 19 Pages |
Abstract
Let V be an n-dimensional inner product space over C, and let H be a subgroup of the symmetric group on {1,â¦,m}. Suppose Ï:HâC is an irreducible character (not necessarily linear). Let VÏm(H) denote the symmetry class of tensors over V associated with H and Ï and let K(T)âEnd(VÏm(H)) be the induced operator of TâEnd(V).It is known that if T is normal, unitary, positive (semi-)definite, Hermitian, then K(T) has the corresponding property. Furthermore, if T1=ξT2 for some ξâC with ξm=1, then K(T1)=K(T2). The converse of these statements are not valid in general. Necessary and sufficient conditions on Ï and the operators T,T1,T2 ensuring the validity of the converses of the above statements are given. These extend the results of those on linear characters by Li and Zaharia.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Chi-Kwong Li, Tin-Yau Tam,