Is it a good idea to name some mathematical objects after my thesis advisor? I am doing my Ph.D. thesis in mathematics. I am wondering if it is a good idea to name some mathematical objects after my thesis advisor. The two objects I have in my mind are:


A representation, whose existence and faithfulness is a main result of my thesis. This representation has not be studied before and thus unnamed. 
A collection of subgroups of a certain group, which have been studied by others but with no specific name assigned to those subgroups.


I did not ask this question directly to my thesis advisor since I believe that out of humility he would decline this request. Have asked this question to a mathematics professor from another university, who personally knows my advisor well and he says that it was a very good idea. But he was somewhat drunk when answering my question and I am wondering if I should take his answer seriously.

Edit: The representation I have mentioned is similar but different from a classical representation, which is named after the mathematician Emil Artin. In this case, should I still call it "Artin's representation", or "(my advisor's surname)'s representation", or leave it unnamed?
It sound as though your advisor was not the first to study/define/use these objects, but rather you just want to name them something, and think it might be nice to name them in honor of your advisor.  Please don't do this.  You'll only contribute to Stigler's law of eponymy, confuse people, embarrass your advisor and/or offend whoever was the first to study these objects.

Bear in mind two things: (i) Not every random object deserves a special name.  (ii) When you name objects, name them in a descriptive and evocative way, that will make using the terms intuitive and non-confusing (as a corollary, it also shouldn't conflict with other notation).  Many people don't even like the idea of name any mathematical objects after people, though it's common practice.

Now that naming them after your advisor is out of the way, you should feel free to consult your advisor on naming these things.