Volume 26, issue 3 (2022)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 27
Issue 6, 2049–2496
Issue 5, 1657–2048
Issue 4, 1273–1655
Issue 3, 823–1272
Issue 2, 417–821
Issue 1, 1–415

Volume 26, 8 issues

Volume 25, 7 issues

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Interests
Editorial Procedure
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Author Index
To Appear
 
Other MSP Journals
A homological model for $U_q\mathfrak{sl}2$ Verma modules and their braid representations

Jules Martel

Geometry & Topology 26 (2022) 1225–1289
Bibliography
1 S Baseilhac, Quantum coadjoint action and the 6j–symbols of Uqsl2, from: "Interactions between hyperbolic geometry, quantum topology and number theory" (editors A Champanerkar, O Dasbach, E Kalfagianni, I Kofman, W Neumann, N Stoltzfus), Contemp. Math. 541, Amer. Math. Soc. (2011) 103 MR2796630
2 S J Bigelow, Braid groups are linear, J. Amer. Math. Soc. 14 (2001) 471 MR1815219
3 S Bigelow, A homological definition of the Jones polynomial, from: "Invariants of knots and 3–manifolds" (editors T Ohtsuki, T Kohno, T Le, J Murakami, J Roberts, V Turaev), Geom. Topol. Monogr. 4, Geom. Topol. Publ. (2002) 29 MR2002601
4 S Bigelow, Homological representations of the Iwahori–Hecke algebra, from: "Proceedings of the Casson Fest" (editors C Gordon, Y Rieck), Geom. Topol. Monogr. 7, Geom. Topol. Publ. (2004) 493 MR2172492
5 V Chari, A Pressley, A guide to quantum groups, Cambridge Univ. Press (1994) MR1300632
6 C De Concini, C Procesi, Quantum groups, from: "D–modules, representation theory, and quantum groups" (editors G Zampieri, A D’Agnolo), Lecture Notes in Math. 1565, Springer (1993) 31 MR1288995
7 V G Drinfeld, Quasi-Hopf algebras, Algebra i Analiz 1 (1989) 114 MR1047964
8 J M Droz, E Wagner, Grid diagrams and Khovanov homology, Algebr. Geom. Topol. 9 (2009) 1275 MR2520400
9 G Felder, C Wieczerkowski, Topological representations of the quantum group Uq(sl2), Comm. Math. Phys. 138 (1991) 583 MR1110457
10 K Habiro, An integral form of the quantized enveloping algebra of sl2 and its completions, J. Pure Appl. Algebra 211 (2007) 265 MR2333771
11 T Ito, Reading the dual Garside length of braids from homological and quantum representations, Comm. Math. Phys. 335 (2015) 345 MR3314507
12 C Jackson, T Kerler, The Lawrence–Krammer–Bigelow representations of the braid groups via Uq(sl2), Adv. Math. 228 (2011) 1689 MR2824566
13 C Kassel, Quantum groups, 155, Springer (1995) MR1321145
14 T Kohno, Monodromy representations of braid groups and Yang–Baxter equations, Ann. Inst. Fourier (Grenoble) 37 (1987) 139 MR927394
15 T Kohno, Hyperplane arrangements, local system homology and iterated integrals, from: "Arrangements of hyperplanes" (editors H Terao, S Yuzvinsky), Adv. Stud. Pure Math. 62, Math. Soc. Japan (2012) 157 MR2933796
16 T Kohno, Quantum and homological representations of braid groups, from: "Configuration spaces" (editors A Bjorner, F Cohen, C De Concini, C Procesi, M Salvetti), CRM Series 14, Ed. Norm. (2012) 355 MR3203647
17 D Krammer, Braid groups are linear, Ann. of Math. 155 (2002) 131 MR1888796
18 R J Lawrence, Homological representations of the Hecke algebra, Comm. Math. Phys. 135 (1990) 141 MR1086755
19 G Lusztig, Finite-dimensional Hopf algebras arising from quantized universal enveloping algebras, J. Amer. Math. Soc. 3 (1990) 257 MR1013053
20 C Manolescu, Nilpotent slices, Hilbert schemes, and the Jones polynomial, Duke Math. J. 132 (2006) 311 MR2219260
21 L Paoluzzi, L Paris, A note on the Lawrence–Krammer–Bigelow representation, Algebr. Geom. Topol. 2 (2002) 499 MR1917064
22 M Salvetti, Topology of the complement of real hyperplanes in N, Invent. Math. 88 (1987) 603 MR884802
23 V V Schechtman, A N Varchenko, Quantum groups and homology of local systems, from: "Algebraic geometry and analytic geometry" (editors A Fujiki, K Kato, T Katsura, Y Kawamata, Y Miyaoka), Springer (1991) 182 MR1260946
24 H Zheng, A reflexive representation of braid groups, J. Knot Theory Ramifications 14 (2005) 467 MR2150743