Is that possible?

And if it is, how?

Not quite sure what you mean

If you have a fixed sidebar on a page and the content of the page goes below the window should the scrolling just move the center and what if you have sidebar content that goes below the bottom of the page? You would never see it.

and are you asking for the sidebar to scroll in the post but not the post?

I would like to have 'position:fixed' sidebars in pages ('body.page'), and scrollable in blog(home page-'body.blog') and single posts ('div.post').

I don't mind the content not being visible, because I have different widgets in pages and posts, in other words, I have thought about that a lot.

so just play with different settings. The sidebars have an ID of 'left', 'left-inner', 'right-inner' and 'right' so you could use something like

body.home #left {position:fixed;}

Oh, great, thanks a lot, I couldn't figure how to call sidebars in CSS