Colored vertex models, colored IRF models and invariants of trivalent colored graphs

Deguchi, Tetsuo; Akutsu, Yasuhiro

doi:10.1143/JPSJ.62.19

Colored vertex models, colored IRF models and invariants of trivalent colored graphs

Tetsuo Deguchi
(
- Tokyo U.
)
,
Yasuhiro Akutsu
(
- Osaka U.
)

Jul 13, 1992

48 pages

Published in:

J.Phys.Soc.Jap. 62 (1993) 19

e-Print:

hep-th/9206057 [hep-th]

DOI:

10.1143/JPSJ.62.19

Report number:

PRINT-92-0241 (TOKYO)

View in:

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Abstract:

We present formulas for the Clebsch-Gordan coefficients and the Racah coefficients for the root of unity representations (

N

-dimensional representations with

q~{2N}=1

) of

U_q(sl(2))

. We discuss colored vertex models and colored IRF (Interaction Round a Face) models from the color representations of

U_q(sl(2))

. We construct invariants of trivalent colored oriented framed graphs from color representations of

U_q(sl(2))

.

References(22)

Figures(0)

A New hierarchy of colored braid group representations

Yasuhiro Akutsu
(
- Osaka U.
)
,
Tetsuo Deguchi
(
- Tokyo U.
)

- Phys.Rev.Lett. 67 (1991) 777-780
•
DOI:
- 10.1103/PhysRevLett.67.777

A General formula for colored Z(n) graded braid matrices and the fusion braid matrices

Tetsuo Deguchi
(
- Tokyo U.
)
,
Yasuhiro Akutsu
(
- Osaka U.
)

- J.Phys.Soc.Jap. 60 (1991) 2559-2570
•
DOI:
- 10.1143/JPSJ.60.2559

- J.Phys.Soc.Jap. 60 4053

- J.Phys.Soc.Jap. 60 3979

Irreducible representations of the quantum analog of SU(2)

P. Roche
(
- Ecole Polytechnique
)
,
D. Arnaudon
(
- Ecole Polytechnique
)

- Lett.Math.Phys. 17 (1989) 295
•
DOI:
- 10.1007/BF00399753

- Progr.Math. 92 471

- Physica 66 279

- Phys.Rev. 179 650

General lattice model of phase transitions

Chungpeng Fan
(
- Rutgers U., Piscataway and
- Northeastern U.
)
,
F.Y. Wu
(
- Rutgers U., Piscataway and
- Northeastern U.
)

- Phys.Rev.B 2 (1970) 723-733
•
DOI:
- 10.1103/PhysRevB.2.723

- J.Phys.Soc.Jap. 58 3441

Graded Solutions of the {Yang-Baxter} Relation and Link Polynomials

Tetsuo Deguchi
(
- Tokyo U., Komaba
)
,
Yasuhiro Akutsu
(
- Kanagawa U.
)

- J.Phys.A 23 (1990) 1861-1876
•
DOI:
- 10.1088/0305-4470/23/11/014

Solvable $Q$ State Models in Lattice Statistics and Quantum Field Theory

C.L. Schultz
(
- SUNY, Stony Brook
)

- Phys.Rev.Lett. 46 (1981) 629-632
•
DOI:
- 10.1103/PhysRevLett.46.629

New families of commuting transfer matrices in q state vertex models

- Phys.Lett.A 84 (1981) 407-410
•
DOI:
- 10.1016/0375-9601(81)90994-4

On the solution of the Yang-Baxter equation

- J.Sov.Math. 19 (1982) 1596-1620,
- Zap.Nauchn.Semin. 95 (1980) 129-160
•
DOI:
- 10.1007/BF01091463

A q difference analog of U(g) and the Yang-Baxter equation

Michio Jimbo
(
- Kyoto U., RIMS
)

- Lett.Math.Phys. 10 (1985) 63-69
•
DOI:
- 10.1007/BF00704588

- J.Math.Phys. 30 2397

Fusion rules and R matrix for the composition of regular spins with semiperiodic representations of SL(2)-q

Daniel Arnaudon
(
- Ecole Polytechnique
)

- Phys.Lett.B 268 (1991) 217-221
•
DOI:
- 10.1016/0370-2693(91)90806-2

Quantum r Matrix for the Generalized Toda System

Michio Jimbo
(
- Kyoto U., RIMS
)

- Commun.Math.Phys. 102 (1986) 537-547
•
DOI:
- 10.1007/BF01221646

- Commun.Math.Phys. 118 335

- J.Phys.Soc.Jap. 58 2694

Ribbon graphs and their invariants derived from quantum groups

- Commun.Math.Phys. 127 (1990) 1-26
•
DOI:
- 10.1007/BF02096491

- Trans.Am.Math.Soc. 318 317