In Rotation Matrices for Real Spherical Harmonics. Direct Determination by Recursion, I can almost completely understand the recurrence relations described, but for one part.
The $Y^l_m$ function is as usually defined for real spherical harmonics, as here.
Early in the paper, however, the author states:
$ \langle Y_{lm} | Y _{\lambda\mu} \rangle = \delta_{l\lambda} \delta _{m\mu} $
Not for slack, but purely as background information, I'm a computer scientist. I like to understand math as much as I absolutely minimally need can. I only have a vague understanding of what this means - it is the presentation of a group.
But practically what does this mean for the $\delta$ function when it is used later in the paper? For example, later in the paper (in the actual recurrence relations 6.3-6.6) we see use of $\delta_{m1}$. Does it means $Y_{lm}$ equals $\delta_{lm}$?