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Lefschetz property, Schur-Weyl duality and a \(q\)-deformation of Specht polynomial. (English) Zbl 1125.20001
The paper under review studies the well-known Schur-Weyl duality between the quantum group \(U_q(sl_d)\) and the Hecke algebra \(H\) associated to the symmetric group \(S_n\) when \(q\) is generic. The main result is a description of the generators of each irreducible \(U_q(sl_d)\)-\(H\) bimodule in terms of certain \(q\)-analogues of Specht polynomials. The author also uses the Leftschetz property to construct a linear basis of the irreducible \(U_q(sl_d)\)-submodule inside the \(n\)-tensor space when \(d=2\).
Reviewer: Hu Jun (Beijing)

MSC:
20C08 Hecke algebras and their representations
17B37 Quantum groups (quantized enveloping algebras) and related deformations
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