help for hans wegner "the chair" (maybe!)  

Well now.  Here's another chair, likely from the same batch, that was sold on 1st dibbs.  (I referred earlier to JP Morgan, but of course, the chair's inventory is from Chase Manhattan.  They later merged.
https://www.1stdibs.com/furniture/seating/office-chairs-desk-chairs/hans...

I'm no wood ID expert but I'm pretty sure that Dibs chair isn't oak.  It's also very shiny.  Looks redone.
The OP's chair looks like it has a finish added to the original, which is now chipping off on the top of the arms. Lacquer chips like this instead of wearing off gradually, evenly like varnish or stain.  Not that I'm a finish expert, either.  Just throwing it out there.

From the pictures you have shown it looks authentic. But what if it is not authentic it is beautiful all the way. You havent made any wrong choice. A chair of 50's is itself a stamp of authenticity.
Edited by DA (no advertising in your comments please)

I agree with Spanky that the chair shown on 1st Dibs is almost certainly not oak.  I do not know what the wood is, but it looks like maple. 
The 1st Dibs chair is claimed to be one that was owned by Chase Manhattan.  It is problematic in that the arms and backrest appear to be made not of three distinct pieces of wood that have been finger-jointed together, but rather the arms and backrest are made of multiple pieces of wood that have been laminated together, with numerous glue joints.  This is typical of knock-off furniture, since large pieces of hardwood are quite expensive, and it costs a lot less to make a large piece of wood by gluing together smaller pieces.
To my knowledge, no licensed producer of Hans Wegner's "the chair" ever did this. 

Tchp: I agree, that looks like maple. And the laminated back and arms are not what I've seen in any Johannes Hansen or PP Møbler production. 
This is a fine point, but the joints between the legs and the back and arms, which is where the grain meets at 90 degrees are supposed to be emphasized by having the opposing pieces of wood sanded round slightly at the joint. (This is because the different pieces of wood move in different directions here, so smooth sanded joint at the factory would no longer be smooth when it got to the customer. It would look very poorly made.  Wegner's solution was to obscure the "problem" by emphasizing the joint. A very clever trick, both of psychology and of woodcraft).
This other Chase Bank chair lacks that detail:

And other knock-off for sale on the internet at a site specializing in reproductions, with the backrest made of at least three pieces of wood, and the arms also appearing to be made of numerous pieces of wood laminated together.  The front seat support stretcher also appears to have a lamination seam, so even it is probably not a single piece of natural wood.
Of note is that the fingerjoint style of joinery is used in the arms/backrest on knockoffs like this, so the presence of the fingerjoint does not guarantee authenticity. 

And yes, the presence of that finger joint on the back proves nothing much. But the absence would prove a lot.
Note this second knockoff also lacks the correct leg to arm emphasized joint.  

So, back to the OP's chair---it looks like it has a wood seat under that black cambric that is coming off.  Does the Wegner chair have a wood seat or is it a wood frame with webbing?  In my experience, lower end chairs have wood seats and high end chairs have frame seats with either jute or elastic webbing or a single piece of stretchy mesh fabric over the whole frame.  A wood seat with a layer of thin foam as would be appropriate for The Chair would not be as nearly as comfortable as webbing.
The photo Leif posted shows a fabric covering under the seat, as do others I have seen online.  Usually this is done to cover webbing and prevent bits of foam from dusting the floor below as the foam wears against the webbing.  I guess on a high end chair the fabric could also just provide a more finished look.  
 
edited to add:  Never mind!  it's all wood.  I forgot that I had bookmarked the Youtube video about how this chair is made.  Shoulda just looked at that first before spouting off.

Huh.  That video leaves out the steps in which the band-sawn blanks are shaped on the copy lathe, the zig-zag joint is made, the hoop is glued up and then shaped on the CNC machine . . .

Nice Spanky. Great video. 

Thank you all for the help! in fact I thought the same thing that he thought vivian: why jp morgan have Purchased at knock-off production? I think also that the angles under the seat are the work of the previous owner carpenter. Original or not original history of this chair is equally fascinating!I removed the metal plate but there is nothing underneath. only the "h" branded. I try to post more images more detailed.

Why would a big bank want to save money on redecorating ?  Hmm . . .
 
"Mr Architect, do we really want to spend $800* per chair if there's a less expensive alternative ?"
"Well, George, I'll see if we can have these made for less -- after all, we're ordering 420* of the things . . . !"
* figures are imaginary . . .

^SDR - That is an excellent point -
Contract / commercial / large quantity standards or particulars of construction may vary from "regular" residential fine furniture standards.

Right.  I'm not suggesting that PP Mobler would make an inferior version of the chair, but that a knock-off manufacturer might be found . . .
 
I should add that a heck of a lot of effort went into preparing Wegner's design for manufacture -- and that anyone intending to knock it off had better be prepared to lose their shirt if they hope to make a profit while offering the chair for a considerably reduced price.

This is an anecdote that may or may not directly relate to this chair.  But there was a time when Georg Jensen was the exclusive retailer for Wegner designs from SalesCo (Carl Hansen et al).  This resulted in a US markup of 3x to 4x over Denmark prices.  Apparently many interior designs and such were less than pleased, and tried to get around Georg Jensen by ordering directly from Denmark, but to no avail.  
In such a case, I could very, very easily see the decorator going to a knock-off for significantly less.