RequestPermissions and switching states

If I request permissions and the avatar grants them within the default state, and then I switch to a different state, are those granted permissions still in effect?

Yes
Permissions are granted to a script as a whole, not a state.

Following script demonstrates this:

default
{
    state_entry()
    {
        llRequestPermissions(llGetOwner(), PERMISSION_TRIGGER_ANIMATION);
    }

    run_time_permissions(integer perms)
    {
        if(perms & PERMISSION_TRIGGER_ANIMATION)
        state other;
    }
}
state other
{
    state_entry()
    {
        if(llGetPermissions() & PERMISSION_TRIGGER_ANIMATION)
        {
            llSay(0, "Has permission still");
        } else {
            llSay(0, "Not got permissions");
        }
    }
}

Thanks very much!