I am pretty sure the Luminosty in Photoshop is defined as: 0.3*R + 0.59*G + 0.11*B
A little experiment:
1) I created a new picture and put a color to a layer.
2) There are few ways to find the RGB values of the color (Color picker, eyedroppertool, info palet). It's easy to compute with hand the lumonisity.
3) Open Histogram palet. Luminosity value is given here by Photoshop if you choose the Luminosity channel.
My conclusion is: Above formula for Luminosity is what Photoshop uses.
I think I understand if a change in luminosity also effects saturation if Hue is constant.
If I simply think about these colorspaces: H, S, B and Hue, Saturation, Luminosity
And define Hue as constant... Then S and B equals to S and L (to keep the same color).
As Brightness and Luminosity are not the same, the saturation has to change.
Some sites imply Luminosity and Brightness are interchangeable (the way I read it at least).