Representation theory resources and references

Representation theory of finite groups

C.Teleman, Representation theory
P.Webb, Representation Theory Book
P.Diaconis, Group representations in probability and statistics
W.Miller, Symmetry, Groups and Their Applications
A.Baker, Representations of finite groups
A.N.Sengupta, Notes on representations of algebras and finite groups
D.M.Jackson, Notes on the representation theory of finite groups
P.Garrett, Representations of GL(2) and SL(2) over finite fields
D.Joyner, Notes on trace formulas for finite groups
T.Y.Lam, Representations of finite groups: A hundred years, Part I  Part II
T.Deshpande, Representations of finite groups of Lie type
Groups and representation theory notes   Topics in representation theory
D.Panyushev, Lectures on representations of finite groups and invariant theory
Materials and links from a course on representation theory at Stanford University
J.Rabinoff, Fourier analysis on finite groups and Schur orthogonality
Wiki page on reps of finite groups
Jeremy Rickard's webpage for a rep theory course contains problem sets and solutions.
Exercises for Joseph Bernstein's course
My course on reps of finite groups

Representations of the symmetric group

P.Diaconis, Representation Theory of the Symmetric Group
W.Miller, Chapter 4. Representations of the symmetric groups
W. Crawley-Boevey, Lectures on representation theory and invariant theory
D.Goldschmidt, Group Characters, Symmetric Functions, and the Hecke Algebra
E.B.Vinberg: Representation of the symmetric groups, a very short summary for SpringerLink. Notice interesting comments that follow the summary.

A.Vershik, A.Okounkov, A New Approach to the Representation Theory of the Symmetric Groups
M.Srinivasan, Notes on the Vershik-Okounkov approach to the representation theory of the symmetric group
A.Vershik, A new approach to the representation theory of the symmetric groups, III: Induced representations and the Frobenius--Young correspondence

Hecke algebras and their representations

O.Ogievetsky, P.Pyatov, Lecture on Hecke algebras
D.Goldschmidt, Group Characters, Symmetric Functions, and the Hecke Algebra
A.Mathas, Hecke algebras and Schur algebras of the symmetric group

McKay correspondence

J. van Hoboken, Platonic solids, binary polyhedral groups, Kleinian singularities and Lie algebras of type A,D,E. Master's Thesis.
R. Stekolshchik, Notes on Coxeter Transformations and the McKay correspondence

Lie groups, Lie algebras, and their representations

Alexander Kirillov, Jr., Introduction to Lie groups and Lie algebras
Dragan Milicic, Lectures on Lie Groups
Shlomo Sternberg, Lie Algebras

Brian Hall, An Elementary Introduction to Groups and Representations
Peter Woit, Lie groups and representations
Notes for Lie algebras class by Victor Kac.
Hans Samelson, Notes on Lie algebras
Eckhard Meinrenken, Clifford algebras and Lie groups
A brief summary Root systems and Weyl groups, by Jeffrey Adams.
Online notes for MIT course Introduction to Lie groups

H.Kraft, C.Procesi, Classical invariant theory. A primer.

P.Cvitanovic, Group theory. Birdtrack's, Lie's, and exceptional groups.
David Vogan has notes on several Lie group topics on his webpage.
P.Garrett, Notes on miscellaneous Lie algebras and groups topics
W.G.Dwyer and C.W.Wilkerson, The elementary geometric structure of compact Lie groups.

Fourier transform on groups and applications

P.Diaconis, Group representations in probability and statistics
M.Mackey, Harmonic analysis as the exploitation of symmetry--a historical survey

Homological algebra

P.May, Notes on Tor and Ext
C.Kassel, Homology and cohomology of associative algebras - A concise introduction to cyclic homology
D.Milicic, Lectures on derived categories
D.Kaledin, Homological methods in Non-commutative Geometry

Highest weight categories

J.Bernstein, I.Gelfand, S.Gelfand, Structure of representations generated by vectors of highest weight
J.Bernstein, I.Gelfand, S.Gelfand,On some category of g-modules
J.Bernstein, S.Gelfand, Tensor products of finite and infinite dimensional representations of semisimple Lie algebras
D.Gaitsgory, Geometric Representation theory Notes for a course on highest weight categories.

Representations of quivers

J.Bernstein, I.Gelfand, V.Ponomarev, Coxeter functors and Gabriel's theorem
W.Crawley-Boevey, Lectures on representations of quivers
H.Derksen, J.Weyman, Quiver representations
M.Brion, Representations of quivers
M.Barot, Representations of quivers
H.Krause, Representations of quivers via reflection functors
W.Crawley-Boevey, More lectures on representations of quivers

L.Le Bruyn, Noncommutative geometry @n


L.Nicolaescu, The derived category of sheaves and the Poincare-Verdier duality
J.Bernstein, V.Luntz, Equivariant sheaves and functors 1 2 3 4 5 6
Etale Cohomology resources


D.Milicic, Lectures on algebraic theory of D-modules
J.Bernstein, Algebraic theory of D-modules
J.-P.Schneiders, An introduction to D-modules
P.Maisonobe, C.Sabbah, Aspects of the theory of D-modules
D.Arapura, Notes on D-modules and connections with Hodge theory

Geometric representation theory

Geometric Langlands seminar webpage
V.Ginzburg, Geometric methods in representation theory of Hecke algebras and quantum groups
V.Ginzburg, Lectures on Nakajima's quiver varieties
E.Frenkel, Lectures on the Langlands Program and Conformal Field Theory


Automorphic forms, representations, and L-functions
R.Baxter Exactly Solved Models in Statistical mechanics
A.Molev, Yangians and their applications
A.Molev, M.Nazarov and G.Olshanskii, Yangians and classical Lie algebras