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Dual canonical bases, quantum shuffles and q-characters
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abstract
Rosso and Green have shown how to embed the positive part $U_q(n)$ of a quantum enveloping algebra $U_q(g)$ in a quantum shuffle algebra. In this paper we study some properties of the image of the dual canonical basis $B^*$ of $U_q(n)$ under this embedding $\Phi$. This is motivated by the fact that when $g$ is of type $A_r$, the elements of $\Phi(B^*)$ are $q$-analogues of irreducible characters of the affine Iwahori-Hecke algebras attached to the groups $GL(m)$ over a $p$-adic field.
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Cited by 1 Pith paper
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Freidel-Maillet type equations on fused K-matrices over the positive part of $U_q(\widehat{\mathfrak{sl}}_2)$
Fused K-matrices with explicit Catalan-word entries satisfy Freidel-Maillet type equations for all dimensions 2j+1.
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