What is the notation about group differences in terms standard deviations? I am just getting into watching psych lectures and things online and am taking notes but I have been wondering what the proper/standard way of writing in note form about standard deviations is.

For example: GROUP-A is a third of a standard deviation higher in TRAIT than GROUP-B.

Is there a standardised way of representing that information with a kind of notation or shorthand in psychology?

Thanks! And sorry for the very basic question!
The psychology notation for standardized differences between group means is d. I.e., the difference between group differences divided by the within-group standard deviation. Note that there are some variants about which group is used or whether a pooled standard deviation is obtained.

I.e., in your example: d = 0.3.

If you want to report means and sds, then you typically use M and SD.