1) Follow up with the Hiring Executive, once a week. Show interest and persistence. *Be very careful NOT to convey desperation. That's a major turn-off. Signals something may be wrong with you.
2) The recruiter may have an active slate of qualified candidates already. Hopefully he received your CV. But time kills deals. If he hasn't responded, you're NOT his priority. General rule, the Bigger the company, the slower, more bureaucratic, and dumber they are.
3) Defeat desperation by coming up with more prospects. Focus your energy there. Identify and reach out to profiles just like Senior Mgr IT. Linkedin is a great place to do this research.
Sorry. Waiting sucks!
JSeymourATL gave some good advice IMO.
If this is even a moderately larger organization you can easily get lost in the shuffle and the hiring manager may not even know this because he thought it was all taken care of. In fact, he could wonder why he hasn't heard from "that guy he talked to" and then blow you off later because you never followed up. It is a delicate balance between stalking and diligent persistence but trust me persistence pays off.
Also, I do agree with gamechngr and others that the larger the organization the longer it can take to get a response. 1-2 weeks is not abnormal at all. Also, think about it this way, the recruiter could be out sick for a few days or whatever, and then has a stack of work to do when s/he returns.
One option is to follow up with the manager in a week and just ask for the contact of the recruiter so you may follow up with them as you understand that as a manager they have a lot of priorities to balance, or something along those lines. This assumes you don't already have the recruiters information, and if you do, start following up with them weekly.
Following up in a a week (if small) or two is exactly what I would do, but my original post was just to say "don't rush it". Most of my offers have taken 3 weeks to get the appointment and another three - four weeks to get to the sign or walk stage. I have mostly looked into bigger companies though.
Of course, some HR departments (usually at huge companies) simply work at a glacial pace. I've had recruiters call me weeks after the hiring manager and I had agreed on salary and dates telling me that I still had to go through their process (I didn't in the end take that job, btw).
Good luck, and stop fixating on the idea that there's one "best" job or one "best" company. That's not how the world works.