Two Hermitian idempotents of the group algebra

We will choose arbitrarily to work with the first of the standard tableaux of a given partition. With this we can form the two Hermitian algebra elements 

Any tableau would do, but we only need one. This choice serves. 

We stated at the end of Seetion 5.4.3 that f/g)ffV or f/g)VM, g = n, will serve as an idempotent element of the algebra assoeiated with the partition upon which they are based, although these are, of course, notHermitian. This means that 

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