Representations of finite groups

Call number: | 92198 | |

Room/Time: | MW 1:10pm--2:25pm, 520 Math | |

Instructor: | Mikhail Khovanov | |

Office: | 517 Math | |

Office Hours: | Walk-in or by appointment | |

E-mail: | khovanov@math.columbia.edu | |

TA: | Qi You | |

Discussions: | Monday 9-10am, Room 622 | |

Office Hours: | Tue 6-7pm or by appointment, Room 610 | |

E-mail: | yq2121@math.columbia.edu | |

Midterm: | Wednesday, Nov 4 | |

Final: | Monday, Dec 21, 1:10pm-4pm, MAT 520 | |

Webpage: | www.math.columbia.edu/~khovanov/finite | |

P.Webb, Representation Theory Book We need the first 5 sections (pages 1-62).

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.Etingof et al. Introduction to representation theory also discusses category theory, Dynkin diagrams, and representations of quivers.

Qi You's notes on the McKay correspondence

There is at least a dozen textbooks on representations of finite groups in the library---here's
a sample:

J.-P. Serre, * Linear representations of finite groups. *

B. Sagan, * The symmetric group. *

B. Simon, * Representations of finite and compact groups. *

G.James and M.Liebeck, *Representations and characters of groups*.

Modules over rings and algebras, simple modules, Schur's lemma.

Actions of groups on vector spaces, representations.

Group algebras, modules, complete reducibility, Wedderburn's theorem.

Characters, orthogonality relations.

Tensor product of representations.

Restriction and induction.

Applications of representation theory.

Category theory.

The McKay correspondence, Dynkin diagrams, reflection groups.

Representations of the symmetric group.

Representations of quivers.

P.Diaconis, Group representations in probability and statistics

W.Miller, Symmetry, Groups and Their Applications

J.Rabinoff, Fourier analysis on finite groups and Schur orthogonality

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

Wiki page on reps of finite groups

Materials and links from a course on representation theory at Stanford University

Jeremy Rickard's webpage for a rep theory course

Exercises for Joseph Bernstein's course

Notes on Algebra, by Marc Culler Treats rings, modules, modules over PIDs.

A lecture by Daniel Katz on free modules

Condensed review of groups, rings, and modules by Roy Smith

Notes on modules and rings by William Schmitt

Wikipedia's entry on modules

Notes by Ralph Howard

Category theory links: 1 2 3 4 5