New hierarchy of colored-braid-group representations. (English) Zbl 0990.82518
Summary: Novel solutions of the Yang-Baxter relation for a series of multistate vertex models are presented in the braid-group limit. The obtained family of solutions gives a sequence of “colored”-braid-group representations. Possible generalizations of the multivariable Alexander polynomial are discussed.
References:
| [1] | V. F. R. Jones, Bull. Amer. Math. Soc. 12 pp 103– (1985) · Zbl 0564.57006 · doi:10.1090/S0273-0979-1985-15304-2 |
| [2] | Y. Akutsu, J. Phys. Soc. Jpn. 56 pp 839– (1987) · Zbl 0719.57002 · doi:10.1143/JPSJ.56.839 |
| [3] | V. G. Turaev, Invent. Math. 92 pp 527– (1988) · Zbl 0648.57003 · doi:10.1007/BF01393746 |
| [4] | C. N. Yang, Phys. Rev. Lett. 19 pp 1312– (1967) · Zbl 0152.46301 · doi:10.1103/PhysRevLett.19.1312 |
| [5] | R. J. Baxter, in: Exactly Solved Models in Statistical Mechanics (1982) · Zbl 0538.60093 |
| [6] | Y. Akutsu, J. Phys. Soc. Jpn. 56 pp 3039– (1987) · Zbl 0719.57003 · doi:10.1143/JPSJ.56.3039 |
| [7] | Y. Akutsu, J. Phys. Soc. Jpn. 56 pp 3464– (1987) · Zbl 0719.57004 · doi:10.1143/JPSJ.56.3464 |
| [8] | Y. Akutsu, J. Phys. Soc. Jpn. 57 pp 757– (1988) |
| [9] | Y. Akutsu, J. Phys. Soc. Jpn. 57 pp 1173– (1988) |
| [10] | Y. Akutsu, J. Phys. Soc. Jpn. 57 pp 1905– (1988) · Zbl 0719.57006 · doi:10.1143/JPSJ.57.1173 |
| [11] | M. Wadati, Phys. Rep. 180 pp 427– (1989) · doi:10.1016/0370-1573(89)90123-3 |
| [12] | T. Deguchi, Adv. Stud. Pure Math. 19 pp 193– (1989) |
| [13] | J. W. Alexander, Trans. Amer. Math. Soc. 30 pp 275– (1928) · doi:10.1090/S0002-9947-1928-1501429-1 |
| [14] | P. Freyd, Bull. Amer. Math. Soc. 12 pp 239– (1985) · Zbl 0572.57002 · doi:10.1090/S0273-0979-1985-15361-3 |
| [15] | J. H. Przytycki, Kobe J. Math. 4 pp 115– (1987) |
| [16] | B. U. Felderhof, Physica (Utrecht) 66 pp 279– (1973) · doi:10.1016/0031-8914(73)90330-3 |
| [17] | K. Sogo, Prog. Theor. Phys. 68 pp 508– (1982) · Zbl 1073.82546 · doi:10.1143/PTP.68.508 |
| [18] | C. Fan, Phys. Rev. 179 pp 650– (1969) |
| [19] | C. Fan, Phys. Rev. B 2 pp 723– (1970) · doi:10.1103/PhysRevB.2.723 |
| [20] | J. W. Alexander, Proc. Natl. Acad. Sci. 9 pp 93– (1923) · doi:10.1073/pnas.9.3.93 |
| [21] | A. A. Markov, Moscou 1 pp 73– (1935) |
| [22] | K. Sogo, Prog. Theor. Phys. 70 pp 730– (1983) · Zbl 1098.82548 · doi:10.1143/PTP.70.730 |
| [23] | K. Sogo, Prog. Theor. Phys. 70 pp 739– (1983) · doi:10.1143/PTP.70.739 |
| [24] | T. Deguchi, J. Phys. Soc. Jpn. 58 pp 3441– (1989) · doi:10.1143/JPSJ.58.3441 |
| [25] | T. Deguchi, J. Phys. A 23 pp 1861– (1990) · Zbl 0724.57002 · doi:10.1088/0305-4470/23/11/014 |
| [26] | P. P. Kulish, J. Soviet Math. 19 pp 1596– (1982) · Zbl 0553.58039 · doi:10.1007/BF01091463 |
| [27] | Y. Akutsu, Commun. Math. Phys. 117 pp 243– (1988) · Zbl 0651.57005 · doi:10.1007/BF01223592 |
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