Algebraic & Geometric Topology Volume 5, issue 1 (2005)

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the Journal

Editorial Board

Editorial Interests

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN (electronic): 1472-2739

ISSN (print): 1472-2747

Other MSP Journals

Infinitely many two-variable generalisations of the Alexander–Conway polynomial

David De Wit, Atsushi Ishii and Jon Links

Algebraic & Geometric Topology 5 (2005) 405–418

DOI: 10.2140/agt.2005.5.405

Bibliography

1	B Abdesselam, D Arnaudon, A Chakrabarti, Representations of 𝒰_q(sl(N)) at roots of unity, J. Phys. A 28 (1995) 5495 MR1364366
2	D De Wit, Automatic evaluation of the Links–Gould invariant for all prime knots of up to 10 crossings, J. Knot Theory Ramifications 9 (2000) 311 MR1753798
3	D De Wit, An infinite suite of Links–Gould invariants, J. Knot Theory Ramifications 10 (2001) 37 MR1822139
4	D De Wit, Automatic construction of explicit R matrices for the one-parameter families of irreducible typical highest weight (⋅0_m\|⋅α_n) representations of U_q[gl(m\|n)], Comput. Phys. Comm. 145 (2002) 205 MR1905732
5	D De Wit, J R Links, L H Kauffman, On the Links–Gould invariant of links, J. Knot Theory Ramifications 8 (1999) 165 MR1687549
6	P Freyd, D Yetter, J Hoste, W B R Lickorish, K Millett, A Ocneanu, A new polynomial invariant of knots and links, Bull. Amer. Math. Soc. (N.S.) 12 (1985) 239 MR776477
7	M D Gould, J R Links, Y Z Zhang, Type–I quantum superalgebras, q–supertrace, and two-variable link polynomials, J. Math. Phys. 37 (1996) 987 MR1371053
8	A Ishii, The Links–Gould invariant of closed 3–braids, J. Knot Theory Ramifications 13 (2004) 41 MR2039117
9	A Ishii, Algebraic links and skein relations of the Links–Gould invariant, Proc. Amer. Math. Soc. 132 (2004) 3741 MR2084099
10	A Ishii, The Links–Gould polynomial as a generalization of the Alexander–Conway polynomial, Pacific J. Math. 225 (2006) 273 MR2233736
11	A Ishii, T Kanenobu, Different links with the same Links–Gould invariant, Osaka J. Math. 42 (2005) 273 MR2147736
12	V Kac, Representations of classical Lie superalgebras, from: "Differential geometrical methods in mathematical physics, II (Proc. Conf., Univ. Bonn, Bonn, 1977)", Lecture Notes in Math. 676, Springer (1978) 597 MR519631
13	L H Kauffman, H Saleur, Free fermions and the Alexander–Conway polynomial, Comm. Math. Phys. 141 (1991) 293 MR1133269
14	J R Links, M D Gould, Two variable link polynomials from quantum supergroups, Lett. Math. Phys. 26 (1992) 187 MR1199742
15	J R Links, M D Gould, R B Zhang, Quantum supergroups, link polynomials and representation of the braid generator, Rev. Math. Phys. 5 (1993) 345 MR1223526
16	T Ohtsuki, Quantum invariants, 29, World Scientific Publishing Co. (2002) MR1881401
17	T D Palev, N I Stoilova, J Van der Jeugt, Finite-dimensional representations of the quantum superalgebra U_q[gl(n∕m)] and related q–identities, Comm. Math. Phys. 166 (1994) 367 MR1309554
18	R B Zhang, Finite-dimensional irreducible representations of the quantum supergroup U_q(gl(m∕n)), J. Math. Phys. 34 (1993) 1236 MR1207983
19	R B Zhang, Quantum supergroups and topological invariants of three-manifolds, Rev. Math. Phys. 7 (1995) 809 MR1346290