I have finished my qualifying exam for the PhD in Math, and would like to survey through different advanced Mathematics topics, particularly focusing on Representation Theory and Mathematical Physics.
I would love to ask if someone can recommend me TWO books on the following topics, in particular,
1) the first book is the "Bible" that everyone working in the field should know, and
2) the second book is a "good" introductory book that hopefully provides many examples to demonstate the theory, (since in my opinion most classical "bible" is too abstract and concise to spend time explaining thoroughly the concept...)
-Langlands Program / Duality
-Affine Lie Algebra / Kac Moody / Loop Groups ...
-Vertex (Operator) Algebra
-Non-compact Quantum Groups / Hopf Algebra
-Conformal Field Theory / Quantum Field Theory
-Absolute Galois Group
-Cohomology Theory (in Algebraic Geometry)
-All the physics involving those SO(n,m), SL(n,C), SU(n) in different Spacetime, etc etc (I don't know how to phrase this topic...Gauge Theory?)
Really appreciate your help.