Algebraic & Geometric Topology Volume 21, issue 3 (2021)

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the Journal

Editorial Board

Subscriptions

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1472-2739 (online)

ISSN 1472-2747 (print)

Author Index

To Appear

Other MSP Journals

A combinatorial description of the centralizer algebras connected to the Links–Gould invariant

Cristina Ana-Maria Anghel

Algebraic & Geometric Topology 21 (2021) 1553–1593

DOI: 10.2140/agt.2021.21.1553

Bibliography

1	M Aigner, A course in enumeration, 238, Springer (2007) MR2339282
2	J W Barrett, B W Westbury, Spherical categories, Adv. Math. 143 (1999) 357 MR1686423
3	A Beliakova, C Blanchet, Skein construction of idempotents in Birman–Murakami–Wenzl algebras, Math. Ann. 321 (2001) 347 MR1866492
4	A M Cohen, B Frenk, D B Wales, Brauer algebras of simply laced type, Israel J. Math. 173 (2009) 335 MR2570672
5	A M Cohen, D A H Gijsbers, D B Wales, BMW algebras of simply laced type, J. Algebra 286 (2005) 107 MR2124811
6	A M Cohen, D A H Gijsbers, D B Wales, The Birman–Murakami–Wenzl algebras of type D_n, Comm. Algebra 42 (2014) 22 MR3169552
7	A M Cohen, S Liu, S Yu, Brauer algebras of type C, J. Pure Appl. Algebra 216 (2012) 407 MR2835205
8	D De Wit, J R Links, L H Kauffman, On the Links–Gould invariant of links, J. Knot Theory Ramifications 8 (1999) 165 MR1687549
9	N Geer, B Patureau-Mirand, Multivariable link invariants arising from 𝔰𝔩(2\|1) and the Alexander polynomial, J. Pure Appl. Algebra 210 (2007) 283 MR2311186
10	N Geer, B Patureau-Mirand, On the colored HOMFLY-PT, multivariable and Kashaev link invariants, Commun. Contemp. Math. 10 (2008) 993 MR2468374
11	A Ishii, The Links–Gould invariant of closed 3–braids, J. Knot Theory Ramifications 13 (2004) 41 MR2039117
12	A Ishii, The Links–Gould polynomial as a generalization of the Alexander–Conway polynomial, Pacific J. Math. 225 (2006) 273 MR2233736
13	V F R Jones, Index for subfactors, Invent. Math. 72 (1983) 1 MR696688
14	V F R Jones, A polynomial invariant for knots via von Neumann algebras, Bull. Amer. Math. Soc. 12 (1985) 103 MR766964
15	V F R Jones, Hecke algebra representations of braid groups and link polynomials, Ann. of Math. 126 (1987) 335 MR908150
16	L H Kauffman, State models and the Jones polynomial, Topology 26 (1987) 395 MR899057
17	S M Khoroshkin, V N Tolstoy, Universal R–matrix for quantized (super)algebras, Comm. Math. Phys. 141 (1991) 599 MR1134942
18	B M Kohli, On the Links–Gould invariant and the square of the Alexander polynomial, J. Knot Theory Ramifications 25 (2016) MR3463851
19	M Kosuda, J Murakami, Centralizer algebras of the mixed tensor representations of quantum group U_q(gl(n,C)), Osaka J. Math. 30 (1993) 475 MR1240008
20	G I Lehrer, R B Zhang, Strongly multiplicity free modules for Lie algebras and quantum groups, J. Algebra 306 (2006) 138 MR2271576
21	J R Links, M D Gould, Two variable link polynomials from quantum supergroups, Lett. Math. Phys. 26 (1992) 187 MR1199742
22	I Marin, E Wagner, A cubic defining algebra for the Links–Gould polynomial, Adv. Math. 248 (2013) 1332 MR3107542
23	J Murakami, The Kauffman polynomial of links and representation theory, Osaka J. Math. 24 (1987) 745 MR927059
24	J Murakami, The representations of the q–analogue of Brauer’s centralizer algebras and the Kauffman polynomial of links, Publ. Res. Inst. Math. Sci. 26 (1990) 935 MR1079902
25	A Ram, H Wenzl, Matrix units for centralizer algebras, J. Algebra 145 (1992) 378 MR1144939
26	R P Stanley, Enumerative combinatorics, II, 62, Cambridge Univ. Press (1999) MR1676282
27	D Stanton, D White, Constructive combinatorics, Springer (1986) MR843332
28	H N V Temperley, E H Lieb, Relations between the “percolation” and “colouring” problem and other graph-theoretical problems associated with regular planar lattices : some exact results for the “percolation” problem, Proc. Roy. Soc. London Ser. A 322 (1971) 251 MR498284
29	H Wenzl, On the structure of Brauer’s centralizer algebras, Ann. of Math. 128 (1988) 173 MR951511
30	H Yamane, Quantized enveloping algebras associated with simple Lie superalgebras and their universal R–matrices, Publ. Res. Inst. Math. Sci. 30 (1994) 15 MR1266383