Volume 26, issue 3 (2022)

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

Volume 28
Issue 3, 1005–1499
Issue 2, 497–1003
Issue 1, 1–496

Volume 27, 9 issues

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 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