A New hierarchy of colored braid group representations - INSPIRE

DataBETA

A New hierarchy of colored braid group representations

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

Jul 29, 1991

14 pages

Published in:

Phys.Rev.Lett. 67 (1991) 777-780

DOI:

10.1103/PhysRevLett.67.777

Report number:

PRINT-91-0315 (TOKYO)

View in:

reference search24 citations

Citations per year

Abstract: (APS)

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(25)

Figures(0)

A polynomial invariant for knots via von Neumann algebras

V.F.R. Jones
(
- Pennsylvania U.
)

- Bull.Am.Math.Soc. 12 (1985) 103-111
•
DOI:
- 10.1090/S0273-0979-1985-15304-2

Knot invariants and the critical statistical systems

Y. Akutsu
(
- Kanagawa U.
)
,
M. Wadati
(
- Tokyo U., Komaba
)

- J.Phys.Soc.Jap. 56 (1987) 839-842
•
DOI:
- 10.1143/JPSJ.56.839

The Yang-Baxter equation and invariants of links

V.G. Turaev
(
- Steklov Math. Inst., St. Petersburg
)

- Invent.Math. 92 (1988) 527-553
•
DOI:
- 10.1007/BF01393746

Some exact results for the many body problems in one dimension with repulsive delta function interaction

Chen-Ning Yang
(
- SUNY, Stony Brook
)

- Phys.Rev.Lett. 19 (1967) 1312-1314
•
DOI:
- 10.1103/PhysRevLett.19.1312

Exactly Solvable Models and New Link Polynomials. 1. $N$ State Vertex Models

Yasuhiro Akutsu
(
- Kanagawa U.
)
,
Miki Wadati
(
- Tokyo U., Komaba
)

- J.Phys.Soc.Jap. 56 (1987) 3039-3051
•
DOI:
- 10.1143/JPSJ.56.3039

Exactly solvable models and new link polynomials. 2: Link polynomials for closed three braids

- J.Phys.Soc.Jap. 56 (1987) 3464-3479
•
DOI:
- 10.1143/JPSJ.56.3464

Exactly Solvable Models and New Link Polynomials. 3. Two Variable Topological Invariants

- J.Phys.Soc.Jap. 57 (1988) 757-776
•
DOI:
- 10.1143/JPSJ.57.757

Exactly Solvable Models and New Link Polynomials: 4. Irf Models

- J.Phys.Soc.Jap. 57 (1988) 1173-1185
•
DOI:
- 10.1143/JPSJ.57.1173

Exactly Solvable Models and New Link Polynomials. 5. {Yang-Baxter} Operator and Braid Monoid Algebra

- J.Phys.Soc.Jap. 57 (1988) 1905-1923
•
DOI:
- 10.1143/JPSJ.57.1905

- Phys.Rept. 180 427

KNOT THEORY BASED ON SOLVABLE MODELS AT CRITICALITY

- Adv.Stud.Pure Math. 19 (1989) 193-286

- Trans.Am.Math.Soc. 30 275

A new polynomial invariant of knots and links

P. Freyd
(
- Pennsylvania U.
)
,
D. Yetter
(
- Clark U.
)
,
J. Hoste
(
- Rutgers U., Piscataway
)
,
W.B.R. Lickorish
(
- Cambridge U.
)
,
K. Millett
(
- UC, Santa Barbara and
- Berkeley, Math. Sci.-Res. Inst.
)

et al.

- Bull.Am.Math.Soc. 12 (1985) 239-246
•
DOI:
- 10.1090/S0273-0979-1985-15361-3

- Kobe J.Math. 4 115

- Physica 66 279

- Prog.Theor.Phys. 68 508

- 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

- Proc.Nat.Acad.Sci. 9 93

NEW FACTORIZED S MATRIX AND ITS APPLICATION TO EXACTLY SOLVABLE Q STATE MODEL. I

- Prog.Theor.Phys. 70 (1983) 730-738,
- Prog. Theor. Phys. 70 ( 1983) 730-738
•
DOI:
- 10.1143/PTP.70.730

NEW FACTORIZED S MATRIX AND ITS APPLICATION TO EXACTLY SOLVABLE Q STATE MODEL. II

- Prog.Theor.Phys. 70 (1983) 739-746,
- Prog. Theor. Phys. 70 ( 1983) 739-746
•
DOI:
- 10.1143/PTP.70.739

- 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

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

Knots, Links, Braids and Exactly Solvable Models in Statistical Mechanics

Yasuhiro Akutsu
(
- Kanagawa U.
)
,
Miki Wadati
(
- Tokyo U., Komaba
)

- Commun.Math.Phys. 117 (1988) 243
•
DOI:
- 10.1007/BF01223592