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Diamond representations of 𝔰𝔩 ( n )

Didier ArnalNadia Bel BarakaNorman J. Wildberger — 2006

Annales mathématiques Blaise Pascal

In [6], there is a graphic description of any irreducible, finite dimensional 𝔰𝔩 ( 3 ) module. This construction, called diamond representation is very simple and can be easily extended to the space of irreducible finite dimensional 𝒰 q ( 𝔰𝔩 ( 3 ) ) -modules. In the present work, we generalize this construction to 𝔰𝔩 ( n ) . We show it is in fact a description of the reduced shape algebra, a quotient of the shape algebra of 𝔰𝔩 ( n ) . The basis used in [

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