This research demonstrates Schur duality between W(n) and a finite-dimensional algebra, implying significant mathematical connections.
We decompose tensor products of the defining representation of a Cartan type Lie algebra W (n) in the case where the number of tensoring does not exceed the rank of the Lie algebra.As a result, we get a kind of Schur duality between W (n) and a finite dimensional non-semisimple algebra, which is the semi-group ring of the transformation semigroup T m .
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K. Nishiyama (1999) studied this question.
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