Algebraic & Geometric Topology Volume 17, issue 6 (2017)

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Super $q$–Howe duality and web categories

Daniel Tubbenhauer, Pedro Vaz and Paul Wedrich

Algebraic & Geometric Topology 17 (2017) 3703–3749

DOI: 10.2140/agt.2017.17.3703

Bibliography

1	A K Aiston, H R Morton, Idempotents of Hecke algebras of type A, J. Knot Theory Ramifications 7 (1998) 463 MR1633027
2	A Berenstein, S Zwicknagl, Braided symmetric and exterior algebras, Trans. Amer. Math. Soc. 360 (2008) 3429 MR2386232
3	S Cautis, J Kamnitzer, S Morrison, Webs and quantum skew Howe duality, Math. Ann. 360 (2014) 351 MR3263166
4	S J Cheng, W Wang, Howe duality for Lie superalgebras, Compositio Math. 128 (2001) 55 MR1847665
5	H El Turkey, J R Kujawa, Presenting Schur superalgebras, Pacific J. Math. 262 (2013) 285 MR3069063
6	N Geer, B Patureau-Mirand, On the colored HOMFLY–PT, multivariable and Kashaev link invariants, Commun. Contemp. Math. 10 (2008) 993 MR2468374
7	E Gorsky, S Gukov, M Stošić, Quadruply-graded colored homology of knots, preprint (2013) arXiv:1304.3481
8	J Grant, A categorification of the skew Howe action on a representation category of U_q(𝔤𝔩(m\|n)), preprint (2015) arXiv:1504.07671
9	J Grant, A generators and relations description of a representation category of U_q(𝔤𝔩(1\|1)), Algebr. Geom. Topol. 16 (2016) 509 MR3470707
10	S Gukov, M Stošić, Homological algebra of knots and BPS states, from: "Proceedings of the Freedman Fest" (editors R Kirby, V Krushkal, Z Wang), Geom. Topol. Monogr. 18, Geom. Topol. Publ. (2012) 309 MR3084243
11	A Gyoja, A q–analogue of Young symmetrizer, Osaka J. Math. 23 (1986) 841 MR873212
12	R Howe, Perspectives on invariant theory : Schur duality, multiplicity-free actions and beyond, from: "The Schur lectures" (editors I Piatetski-Shapiro, S Gelbart), Israel Math. Conf. Proc. 8, Bar-Ilan Univ. (1995) 1 MR1321638
13	V F R Jones, Hecke algebra representations of braid groups and link polynomials, Ann. of Math. 126 (1987) 335 MR908150
14	L H Kauffman, S L Lins, Temperley–Lieb recoupling theory and invariants of 3–manifolds, 134, Princeton Univ. Press (1994) MR1280463
15	G Kuperberg, Spiders for rank 2 Lie algebras, Comm. Math. Phys. 180 (1996) 109 MR1403861
16	J H Kwon, Crystal bases of q–deformed Kac modules over the quantum superalgebras U_q(𝔤𝔩(m\|n)), Int. Math. Res. Not. 2014 (2014) 512 MR3159079
17	X S Lin, H Zheng, On the Hecke algebras and the colored HOMFLY polynomial, Trans. Amer. Math. Soc. 362 (2010) 1 MR2550143
18	K Liu, P Peng, Proof of the Labastida–Mariño–Ooguri–Vafa conjecture, J. Differential Geom. 85 (2010) 479 MR2739811
19	S Lukac, Homfly skeins and the Hopf link, PhD thesis, University of Liverpool (2001)
20	G Lusztig, Introduction to quantum groups, 110, Birkhäuser (1993) MR1227098
21	H Mitsuhashi, Schur–Weyl reciprocity between the quantum superalgebra and the Iwahori–Hecke algebra, Algebr. Represent. Theory 9 (2006) 309 MR2251378
22	H Murakami, T Ohtsuki, S Yamada, Homfly polynomial via an invariant of colored plane graphs, Enseign. Math. 44 (1998) 325 MR1659228
23	H Queffelec, A Sartori, Mixed quantum skew Howe duality and link invariants of type A, preprint (2015) arXiv:1504.01225
24	J Rasmussen, Some differentials on Khovanov–Rozansky homology, Geom. Topol. 19 (2015) 3031 MR3447099
25	D E V Rose, D Tubbenhauer, Symmetric webs, Jones–Wenzl recursions, and q–Howe duality, Int. Math. Res. Not. 2016 (2016) 5249 MR3556438
26	G Rumer, E Teller, H Weyl, Eine für die Valenztheorie geeignete Basis der binären Vektorinvarianten, Nachr. Ges. Wiss. Göttingen, Math.-Phys. Kl. 1932 (1932) 499
27	A Sartori, Categorification of tensor powers of the vector representation of U_q(𝔤𝔩(1\|1)), PhD thesis, Universiät Bonn (2014)
28	A Sartori, Categorification of tensor powers of the vector representation of U_q(𝔤𝔩(1\|1)), Selecta Math. 22 (2016) 669 MR3477333
29	V G Turaev, Quantum invariants of knots and 3–manifolds, 18, Walter de Gruyter (2010) MR2654259
30	G Williamson, Singular Soergel bimodules, Int. Math. Res. Not. 2011 (2011) 4555 MR2844932
31	Y Wu, R B Zhang, Unitary highest weight representations of quantum general linear superalgebra, J. Algebra 321 (2009) 3568 MR2510063
32	H Yamane, Quantized enveloping algebras associated with simple Lie superalgebras and their universal R–matrices, Publ. Res. Inst. Math. Sci. 30 (1994) 15 MR1266383
33	R B Zhang, Structure and representations of the quantum general linear supergroup, Comm. Math. Phys. 195 (1998) 525 MR1640999