What question did this study set out to answer?

The study focuses on decomposing tensor products of the defining representation of Cartan type Lie algebra W(n).

March 29, 2026Open Access

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

Abstract

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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Cite This Study

K. Nishiyama (Fri,) studied this question.

synapsesocial.com/papers/69c8c15ade0f0f753b39bd65 https://doi.org/https://doi.org/10.5802/jolt.168

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