- #1
btphysics
- 11
- 0
Hello,I read an article about fo generating mass for the first two generations of quarks by breaking the flavour permutation symmetry S3. In the top of the page 5 of the following article: http://arxiv.org/pdf/hep-ph/9807214v2.pdf ,
they mention that "Mq1 transforms as the mixed symmetry term of the doublet complex
4tensorial representation of the S(3)d diagonal subgroup of SL(3) ⊗ SR(3)". What does this means? What transformations on the left and on the right leave the following matrix invariant:
[tex] \begin{pmatrix} A1 & iA2 &-A1-iA2\\ -iA2& -A1 &A1+iA2\\ -A1+iA2&A1-iA2&0 \end{pmatrix}[/tex]
Best regards.
they mention that "Mq1 transforms as the mixed symmetry term of the doublet complex
4tensorial representation of the S(3)d diagonal subgroup of SL(3) ⊗ SR(3)". What does this means? What transformations on the left and on the right leave the following matrix invariant:
[tex] \begin{pmatrix} A1 & iA2 &-A1-iA2\\ -iA2& -A1 &A1+iA2\\ -A1+iA2&A1-iA2&0 \end{pmatrix}[/tex]
Best regards.