Geodesic
Functional equations for transfer-matrix operators in open Hecke chain models
Teoretičeskaâ i matematičeskaâ fizika, Tome 150 (2007) no. 2, pp. 219-236 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider integrable open chain models formulated in terms of the generators of affine Hecke algebras. We use the fusion procedure to construct the hierarchy of commutative elements, which are analogues of the commutative transfer matrices. These elements satisfy a set of functional relations generalizing functional relations for a family of transfer matrices in solvable spin chain models of the $U_q(gl(n|m))$ type.
Keywords: integrable spin chain model, affine Hecke algebra, Temperley–Lieb algebra
Mots-clés : transfer matrix. 
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A. P. Isaev. Functional equations for transfer-matrix operators in open Hecke chain models. Teoretičeskaâ i matematičeskaâ fizika, Tome 150 (2007) no. 2, pp. 219-236. http://geodesic.mathdoc.fr/item/TMF_2007_150_2_a3/

[1] A. P. Isaev, O. V. Ogievetsky, Nucl. Phys. B, 760 (2007), 167 ; math-ph/0510078 | DOI | MR | Zbl

[2] D. Levi, P. Martin, J. Phys. A, 27 (1994), L521 ; P. P. Kulish, A. I. Mudrov, Lett. Math. Phys., 75:2 (2006), 151 ; math.QA/0508289 | DOI | MR | DOI | MR | Zbl

[3] M. Jimbo, Lett. Math. Phys., 11 (1986), 247 | DOI | MR | Zbl

[4] N. Yu. Reshetikhin, L. A. Takhtadzhyan, L. D. Faddeev, Algebra i analiz, 1:1 (1989), 178 | MR | Zbl

[5] A. P. Isaev, EChAYa, 26 (1995), 1204

[6] P. P. Kulish, N. Yu. Reshetikhin, E. K. Sklyanin, Lett. Math. Phys., 5:5 (1981), 393 ; P. P. Kulish, E. K. Sklyanin, “Quantum spectral transform method. Recent developments”, Integrable Quantum Field Theories, Proc. Symp. (Tvärminne, Finland, 1981), Lecture Notes in Phys., 151, eds. J. Hietarinta, C. Montonen, Springer, Berlin, 1982, 61 | DOI | MR | Zbl | DOI | MR | Zbl

[7] L. Mezinchescu, R. Nepomechie, J. Phys. A, 25 (1992), 2533 | DOI | MR

[8] Y. K. Zhou, Nucl. Phys. B, 458 (1996), 504 ; ; W. L. Yang, R. I. Nepomechie, Y. Z. Zhang, Phys. Lett. B, 633 (2006), 664 ; hep-th/9510095hep-th/0511134 | DOI | MR | Zbl | DOI | MR | Zbl

[9] P. P. Kulish, J. Phys. A, 36 (2003), L489 | DOI | MR | Zbl

[10] E. K. Sklyanin, J. Phys. A, 21 (1988), 2375 | DOI | MR | Zbl

[11] A. P. Isaev, Quantum groups and Yang–Baxter equations, Preprint MPIM (Bonn), MPIM2004-132, 2004; http://www.mpim-bonn.mpg.de/Research/MPIM+Preprint+Series

[12] V. Chari, A. Pressley, A Guide to Quantum Groups, Cambrige Univ. Press, 1994 | MR | Zbl

[13] A. P. Isaev, O. V. Ogievetsky, Czech. J. Physics, 55:11 (2005), 1433 ; O. V. Ogievetsky, P. N. Pyatov, “Lecture on Hecke algebras”, Symmetries and Integrable Systems, Proc. Int. School (Dubna, Russia, 1999), ed. A. N. Sissakian, JINR, Dubna, 2000, 39; Preprint MPIM (Bonn), MPIM2001-40; http://www.mpim-bonn.mpg.de/Research/MPIM+Preprint+Series | DOI | MR

[14] D. Levy, Phys. Rev. Lett., 67 (1991), 1971 ; Int. J. Mod. Phys. A, 6 (1991), 5127 ; P. P. Martin, H. Saleur, Lett. Math. Phys., 30:3 (1994), 189 ; ; P. P. Martin, D. Woodcock, J. Algebra, 225:2 (2000), 957 hep-th/9302094 | DOI | MR | Zbl | DOI | MR | Zbl | DOI | MR | Zbl

[15] E. V. Damaskinskii, P. P. Kulish, M. A. Sokolov, Zapiski nauch. sem. POMI, 224 (1995), 155 ; q-alg/9505001 | MR | Zbl

[16] H. Frahm, N. Slavnov, J. Phys. A, 32 (1999), 1547 | DOI | MR | Zbl