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## Main Question or Discussion Point

Hello everybody,

this is the first thread of mine. I try to recover the decomposition of

the fundamental representation (the 7) of G2 into irreducible representations of

A_2. It is given by

7 = 3 + [tex]\bar {3}[\tex] + 1

It maid be that I didn't understand the procedure, founded by Dynkin, to use the

extended Dynkin diagram.

o

a1 a2 ax

Where the last root is the extension. The weights of the 7 are :

{1, 2},

{1, 1},

{0, 1},

{0, 0},

{0, -1},

{-1, -1},

{-1, -2}

I'am using the Cartan subalgebra {a2,ax} to embed the A_2 in G_2. I think that this is

the point where I do a mistake? Maybe someone could help me with the decompostion.

Thanks for reading

Timb00

this is the first thread of mine. I try to recover the decomposition of

the fundamental representation (the 7) of G2 into irreducible representations of

A_2. It is given by

7 = 3 + [tex]\bar {3}[\tex] + 1

It maid be that I didn't understand the procedure, founded by Dynkin, to use the

extended Dynkin diagram.

o

__==__o--oa1 a2 ax

Where the last root is the extension. The weights of the 7 are :

{1, 2},

{1, 1},

{0, 1},

{0, 0},

{0, -1},

{-1, -1},

{-1, -2}

I'am using the Cartan subalgebra {a2,ax} to embed the A_2 in G_2. I think that this is

the point where I do a mistake? Maybe someone could help me with the decompostion.

Thanks for reading

Timb00