[CSC=common short codes] Mainly because they differ by region/country/carrier, AFAIK.
The only halfway decent sites I've seen are wikipedia (look in the bibliography/footnotes) here: http://en.wikipedia.org/wiki/Short_code
Search for 'common short code(s)' too. That might bring up more info. But contacting the CSCA directly might help as well. It's entirely possible that the lease info is private. Not sure it's like domain names, but I may be incorrect.
Does such a directory exist to look up the recipient/owner of a short code? I tried an internet search and can only find companies selling the service.
Please, no direct internet links, just the name of a company/internet site.