An introduction to the representation theory of Temperley-Lieb algebras

Introduction......Page 5
Diagrams and link states......Page 7
Relation to the Hecke algebra and braid group......Page 11
A central element of `39`42`"613A``45`47`"603ATLn()......Page 13
The extended and reduced affine Temperley-Lieb algebra......Page 15
Standard modules......Page 17
Restricted modules......Page 20
Induced modules......Page 21
The spin representation......Page 24
First link-spin intertwiner......Page 25
Second link-spin intertwiner......Page 30
The dimer representations......Page 32
Overview of `39`42`"613A``45`47`"603ATLn()-modules and their connections......Page 37
The radical of a standard module......Page 39
Gram matrices......Page 41
The cases q = i and q = 1......Page 46
Bratelli diagrams......Page 50
Irreducibility of the radicals......Page 53
Principal indecomposable modules......Page 57
The Heisenberg XXZ spin-12 chain model......Page 63
Connection to the dimer model......Page 64
The structure of the Dimer representation......Page 66
Fully and completely packed loop model......Page 67
The matchmaker representation......Page 69
The singles representation......Page 70
Simple spin representation......Page 73
Reduced spin representation......Page 76
Affine dimer representation......Page 80
Conclusion......Page 83
Populaire samenvatting......Page 85
Bibliography......Page 89
The central element Jn......Page 91
Preliminary representation theory......Page 92