Schur Duality for the Cartan Type Lie Algebra Wn

Key Points

• The study focuses on decomposing tensor products of the defining representation of Cartan type Lie algebra W(n).
• Decomposed tensor products of the defining representation of W(n)
• Considered cases where the number of tensoring does not exceed the rank of the Lie algebra
• Established relationships with a non-semisimple algebra
• Demonstrated a Schur duality between W(n) and the semi-group ring of the transformation semigroup Tm
• Provided insights into the structure of tensor products within the context of these algebras