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Let $\hat{H}_m=\hat{H}_m(q)$ be the Iwahori-Hecke algebra of $GL_m$, see for example, Section 2. The simple $\hat{H}_m$-modules are parametrized by Zelevinsky's multi-segments, See Section 2.2 of the paper.

There is a quantum Schur-Weyl duality between quantum affine algebras and affine Hecke algebras, see for example. So I think $U_q(\widehat{sl}_n)$-modules will correspond to $\hat{H}_m$-modules for some $n$.

The irreducible $U_q(\widehat{sl}_n)$-modules are parametrized by Drinfeld polynomials. Given a simple $U_q(\widehat{sl}_n)$-module $V$ with Drinfeld polynomial $\pi(u)=(\pi_1(u), \ldots, \pi_n(u))$. Let $V'$ be the correpsonding $\hat{H}_m$-module. What is the multi-segment of $V'$?

Thank you very much.

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This is described in equation (5.2) in the paper which follows from the paper: Quantum affine algebras and affine Hecke algebras.

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