I believe this is a variation on "slash" notation.
As per your example, C#(g#)
would normally be written as C#/G#
.
That would mean to play a C# major chord, but with G# as the bass note. This is also called a C# major chord in second inversion, or a C# major chord with the fifth in the bass.
You see, the notes in a C# major chord are C#, E# and G#, which are the root note, the third note, and the fifth note. If you put the E# as the lowest note, that is a C# major chord in first inversion, or a C# major chord with the third in the bass. Putting the G# as the lowest note puts it in second inversion.
In the second chord in your example, C#(f)
, it's less clear, because the note f is not a part of a C# major chord. But the correct way to play it would be to play, in ascending order, F(natural), C#, E# and G#, with the option to leave the C# (the third) out if it sounds too dissonant.
C#(f)
should probably beC#(E#)
.