If a mathematician who doesn't know much about the physicist's jargon and conventions had the curiosity to learn how the so called Standard Model (of particle physics, including SUSY) works, where should (s)he have a look to?
References (if they exist!) written for a mathematical target (so can assume e.g. basic differential geometry, basic Lie group theory…) in a "mathematical style" with rigorous definitions, theorems and proofs would be appreciated.
Best Answer
For the standard model, and in particular for its representation-theoretic aspects (which are crucial), I would refer you to the excellent recent article by John Baez and John Huerta from the Bulletin of the American Mathematical Society which can be found here:
http://www.ams.org/journals/bull/2010-47-03/S0273-0979-10-01294-2/home.html
There are also references to other articles and books here that could lead you further.
If you are interested more generally in quantum field theory and its description for mathematicians (where differential geometry plays a big role, in addition to representation theory), then there is the infamous 2-volume "Quantum Field and Strings: A course for mathematicians" which is written by (mostly) mathematicians. It's not going to necessarily give you the correct physical insight, however. Here are the links:
Volume 1
Volume 2
Other good possibilities are Freed-Uhlenbeck's "Geometry of Quantum Field Theory" from the PCMI (Park City) series, or the gargantuan "Mirror Symmetry" from the Clay Math monographs.