Geodesic
Combinatorial Identities Related to Representations of $U_q(\widetilde{\mathfrak{gl}_2})$
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Mathematical physics. Problems of quantum field theory, Tome 226 (1999), pp. 152-162

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We present certain combinatorial identities related to tensor products of evaluation representations of the quantum loop algebra $U_q(\widetilde{\mathfrak{gl}_2})$ or the elliptic quantum group $E_{\rho,\gamma}(\mathfrak{sl}_2)$. The simplest example of the obtained identities was discovered by N. Jing from the validity of the Serre relations in some vertex representations of quantum Kac–Moody algebras. 
@article{TM_1999_226_a11,
     author = {V. O. Tarasov},
     title = {Combinatorial {Identities} {Related} to {Representations} of $U_q(\widetilde{\mathfrak{gl}_2})$},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {152--162},
     publisher = {mathdoc},
     volume = {226},
     year = {1999},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_1999_226_a11/}
}
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V. O. Tarasov. Combinatorial Identities Related to Representations of $U_q(\widetilde{\mathfrak{gl}_2})$. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Mathematical physics. Problems of quantum field theory, Tome 226 (1999), pp. 152-162. http://geodesic.mathdoc.fr/item/TM_1999_226_a11/