Abstract:

<br>
We will describe in details proofs of theorems for separation of variables

<br>
for all De Concini-Kac-Procesi algebras  and Joseph's localizations of 
quantum 

<br>
groups. Based on those, we describe a classification of the maximal 
spectra of 

<br>
all quantum groups and the methods for it. This settles a question of Goodearl 

<br>
and Zhang asking if all maximal ideals of quantum groups have finite 
codimension.