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arXiv · 2605.22571

Two remarks on decomposition numbers of standard modules for quantum affine $\mathfrak{sl}_2$

Xin Fang·Deniz Kus·Markus Reineke
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Abstract

We use Nakajima's geometric approach to representations of quantum affine algebras and recent results on explicit descriptions of specific canonical basis elements, to derive closed positive formulas for certain decomposition numbers of representations of quantum affine $\mathfrak{sl}_2$. Moreover, we obtain a piecewise-linear closed formula for the $q$-characters of irreducible representations of quantum affine $\mathfrak{sl}_2$.

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Xin Fang, Deniz Kus, Markus Reineke. 2026-05-21. Two remarks on decomposition numbers of standard modules for quantum affine $\mathfrak{sl}_2$. https://arxiv.org/abs/2605.22571

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