![]() ![]() Kazhdan, D., Lusztig, G.: Representations of Coxeter groups and Hecke algebras. Inoue, R., Iyama, O., Keller, B., Kuniba, A., Nakanishi, T.: Periodicities of T-systems and Y-systems, dilogarithm identities, and cluster algebras II: types \(C_r\), \(F_4\), and \(G_2\). Inoue, R., Iyama, O., Keller, B., Kuniba, A., Nakanishi, T.: Periodicities of T-systems and Y-systems, dilogarithm identities, and cluster algebras I: type \(B_r\). Henriques, A.: A periodicity theorem for the octahedron recurrence. Goncharov, A.B., Kenyon, R.: Dimers and cluster integrable systems. Gliozzi, F., Tateo, R.: Thermodynamic Bethe ansatz and three-fold triangulations. Galashin, P., Pylyavskyy, P.: The classification of Zamolodchikov periodic quivers. American Mathematical Society, Providence, RI, (1999)įrenkel, E., Szenes, A.: Thermodynamic Bethe ansatz and dilogarithm identities. In Recent developments in quantum affine algebras and related topics (Raleigh, NC, 1998), volume 248 of Contemp. (2) 158(3), 977–1018 (2003)įrenkel, E., Reshetikhin, N.: The \(q\)-characters of representations of quantum affine algebras and deformations of \(W\)-algebras. (electronic)įomin, S., Zelevinsky, A.: \(Y\)-systems and generalized associahedra. (62)įomin, S., Zelevinsky, A.: Cluster algebras. (39)ĭi Francesco, P., Kedem, R.: \(T\)-systems with boundaries from network solutions. ![]() (43)ĭi Francesco, P.: \(T\)-systems, networks and dimers. Springer, Berlin, Translated from the 1968 French original by Andrew Pressley (2002)īrenti, F.: Unimodal, log-concave and Pólya frequency sequences in combinatorics. For the quivers of type \( \otimes A\) to all other quivers in our classification.Īssem, I., Reutenauer, C., Smith, D.: Friezes. ![]() Conversely, we show that every quiver integrable in this sense is necessarily one of the 19 items in our classification. We conjecture them to exhibit a certain form of integrability, namely, as the T-system dynamics proceeds, the values at each vertex satisfy a linear recurrence. In this paper, we classify all quivers with subadditive labelings. In our previous work we have shown that quivers with strictly subadditive labelings are exactly the quivers exhibiting Zamolodchikov periodicity. Strictly subadditive, subadditive and weakly subadditive labelings of quivers were introduced by the second author, generalizing Vinberg’s definition for undirected graphs. ![]()
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