Notes on representations of finite groups

,  and `39`42`"613A``45`47`"603AHom......Page 4
The group algebra......Page 5
Permutation representations......Page 6
Interwining algebras of permutation representations......Page 7
Projecting onto the invariants......Page 9
Projecting onto the equivariants......Page 10
Maschke's Theorem......Page 11
Interwining and irreducibility......Page 12
Multiplicity......Page 13
The Regular Representation......Page 14
Permutation representations again......Page 15
The number of irreducible representations......Page 16
Conjugate representations......Page 17
Definition and first properties of induced representations......Page 18
Induction and Restriction......Page 19
The Gelfand-Graev representation......Page 21
Cuspidal representations......Page 22
Exterior power representations......Page 23
Grassmannian representations......Page 24
General irreducible representations of Sn......Page 25
More on intertwining algebras......Page 27
Multiplicity-free representations......Page 28
Representations of `39`42`"613A``45`47`"603AGL2(q), again.......Page 29
Tensor products......Page 32
Vector bundles......Page 33
Example: Polynomial representations of `39`42`"613A``45`47`"603ASL2(C)......Page 34
Clifford's theorem......Page 35
Example: Non-abelian groups of order p3......Page 37
The group `39`42`"613A``45`47`"603ASL2(q) and some of its subgroups......Page 38
=-1{1}......Page 39
=-1-.25ex-.25ex-.25ex-.25exf......Page 40
=-1-.25ex-.25ex-.25ex-.25exf......Page 41
Irreducible principal series representations......Page 42
Reducible principal series representations......Page 43
Cuspidal representations......Page 45
The character table for q even......Page 49
The character table for q odd......Page 50
Example: q=3......Page 52
Weil representations of `39`42`"613A``45`47`"603ASL2(3)......Page 53
Example: q=5......Page 55
PSL2(q)......Page 56
PGL2(q)......Page 58
The ring of algebraic integers......Page 59
The center of the group algebra......Page 60
The dimension of an irreducible representation......Page 62
Zeros of characters and Burnsides paqb theorem......Page 63