ABSTRACT
In the previous chapter, given an integer n ≥ 1, we constructed a family of complex algebras ( ℌ z ( n ) ) z ∈ ℂ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315371016/5e644d52-ef68-4f0e-ac73-bbf480af375a/content/eq2835.tif"/> of dimension n!, that are deformations of the symmetric group algebras ℂ S ( n ) = ℌ 1 ( n ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315371016/5e644d52-ef68-4f0e-ac73-bbf480af375a/content/eq2836.tif"/> . Almost all of these algebras have the same representation theory: they are semisimple and write as ℌ z ( n ) = ⊕ λ ∈ Y ( n ) End ℂ ( S z λ ) , https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315371016/5e644d52-ef68-4f0e-ac73-bbf480af375a/content/eq2837.tif"/>
