incorrect irrep labels and dimensions?

[Dongsheng-Wen]

Hello developers,

I gave a try on this space group 180. It looks like the K4 is 2D instead of 1D shown in BCS. Should this be \bar K6?

Thanks,
Dongsheng

[zhangzeyingvv]

The output is correct, this is due to different conventions between MSGCorep (BC) and the BCS website. You can verify this by using showMLGCorep[{180,167},"K"] to display the corep matrices and showKrepBCStoBC[180,"DSG"->True] to check the BC/BCS convention correspondence.

[Dongsheng-Wen]

Great thanks for the clarification.
I took another look at 180.168 for example, $\Gamma_7$ under $6^+_{001}|00\frac{1}{3}$.
The table in BCS shows:

 -i	  0
  0	  i

But the programme showed an opposite sign.

Is this also due to the naming conventions? Could you point me to some more references.

Thanks!

[zhangzeyingvv]

The sign difference is inconsequential since the matrices are equivalent (as can be verified by their identical traces). The specific matrix form can indeed have infinite representations through similarity transformations. You can refer to [G. D. James and M. W. Liebeck, Representations and characters of groups (Cambridge University Press, Cambridge; New York, 2001)]