Introduction to McKay's correspondence

Frédéric Palesi

Description

Niveau: Supérieur, Doctorat, Bac+8
Introduction to McKay's correspondence Frederic Palesi 6th march 2006 Introduction Our purpose in this paper is to introduce the Mc Kay's correspondence which associates to each finite subgroups of SU2(C) (the cyclic groups, the binary diedral groups, the binary tetraedral group, the binary octaedral group and the binary icosaedral group), a simple Lie algebra. We will see that when we calculate the character table of these groups, we can construct a graph which will be similar to the Dynkin diagram of a simple Lie algebra of standard type An, Dn, E6, E7 and E8. In the first part we will study the structure of the subgroups of SU2(C) . In the second part we will calculate character tables and McKay's graphs. And in the last part, we will see a way to find the other Dynkin diagrams of type Bn, Cn, F4, G2 1

• character table


• called irreducible


• v0 ?


• irreducible representation


• su2 ??


• calculate ?0


• mckay's graph


• integers a1


• representation

Sujets

• Character table
• Simple module
• Représentation

Informations

• Publié par: mijec
• Nombre de lectures: 23
• Langue: English

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Introduction

Introduction

to McKay’s correspondence

Fr´ede´ricPalesi

6th march 2006

Our purpose in this paper is to introduce the Mc Kay’s correspondence which associates to each finite subgroups ofSU 2 (C) (the cyclic groups, the binary diedral groups, the binary tetraedral group, the binary octaedral group and the binary icosaedral group), a simple Lie algebra. We will see that when we calculate the character table of these groups, we can construct a graph which will be similar to the Dynkin diagram of a simple Lie algebra of standard typeA n , D n , E 6 , E 7 andE 8 . In the first part we will study the structure of the subgroups ofSU 2 (C) . In the second part we will calculate character tables and McKay’s graphs. And in the last part, we will see a way to find the other Dynkin diagrams of typeB n , C n , F 4 , G 2

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