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Are there good references and introduction of Representation Theory as "Representation Theory in a Nutshell for Physicists"?

For example, we hope that the book/ref contains the "introduction to Representation Theory of Finite Groups/Continuous Groups/Lie groups," or the use of Representation Theory in Particle Physics/High-Energy physics/Condensed Matter/Atomic-Molecule-Optics. For one instance, it can contain Representation theory of familiar Lie groups $SU(N), SO(N), Sp(N)$, $E_8$, etc, and its used in the (beyond-)Standard Model. For more instances, more precisely, in 1984, Jackiw started and introduced 3-cocycle to study monople; since 2000, X G Wen has been using the Projective Representation of Global Symmetry Group $G$ to study the topological phases of quantum matter enhanced with global symmetries. Say in 2+1 spacetime dimension, it is classified by 2-cocycles in 2nd Cohomology Group $H^2(G, A)$ where $A$ is related to the gauge group or anyon sectors of topological phases. Is there any mathematical introduction on the Representation Theory part of the story, other than the thick Group Cohomology theory? Other than the basics, hopefully, there are some final remarks on the more modern development (e.g. Langlands program in a nutshell, etc).

Suppose the readers have the understanding of group theory to:

  1. Lie Algebras In Particle Physics: from Isospin To Unified Theories (Frontiers in Physics), H Georgi

  2. Group Theory in a Nutshell for Physicists, A Zee

p.s. Add more description.


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marked as duplicate by Qmechanic Sep 28 '17 at 5:20

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  • 2
    $\begingroup$ ? Physicists almost exclusively focus on representation theory, and the texts you adduce mash it to a pulp. You seriously expect the Langlands program to fit into a cheat-sheet format? $\endgroup$ – Cosmas Zachos Sep 27 '17 at 22:47