In my mind the two saxophone teachers that had the biggest impact on saxophonists on North America were Joe Allard and Joe Viola. Of course there are other great teachers who were/are also true masters of the horn, but many of them are more firmly based in the classical tradition.
If you look at the great Jazz players of the last generation or two who studied with one or even both of the Joe's, you'll find many of the most influential players in Jazz. Joe Viola and Joe Allard's peers were people like Marcel Mule' and Sigard Rascher, they were invited to the Selmer factory to help the development of the Mark VI and Joe Allard even designed his own Slant Link.
I only wish that I could just have one more lesson with Joe V. I have so many questions that I think only he could answer. Joe seemed to know exactly what was happening inside my mouth when I played.
Mary-Sue just turned me on to the Joe Allard web site, where some of his students write about his teaching methods. Allard's wisdom should be preserved for later generations of saxophonists. Someone should really put a site like this together for Joe Viola too.
This stuff is pure saxophone GOLD!
Joe Allard web site
The Master Speaks: Joe Allard video