Southwest is first with about a 35-40% market share, but American, Delta, and United are in a close race for second with each carrier having about 10-15% market share.
Here are some random statistics about SAN (From way back in 1996, so add a few to some of the numbers).
Total daily non-stop direct flights: 246
Number of cities with non-stop direct flights: 33
Total daily through flights (same plane): 85
Number of cities with daily through flights: 36
Total cities served: 173
Average number of daily airline seats: 28,100
Number of airlines serving Lindbergh Field: 17