Volume 18, issue 1 (2018)

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DAHA and plane curve singularities

Ivan Cherednik and Ian Philipp

Algebraic & Geometric Topology 18 (2018) 333–385
Bibliography
1 M Aganagic, S Shakirov, Refined Chern–Simons theory and knot homology, from: "String-Math 2011" (editors J Block, J Distler, R Donagi, E Sharpe), Proc. Sympos. Pure Math. 85, Amer. Math. Soc. (2012) 3 MR2985324
2 A Beauville, Counting rational curves on K3 surfaces, Duke Math. J. 97 (1999) 99 MR1682284
3 N Bourbaki, Éléments de mathématique, XXXIV : Groupes et algèbres de Lie, Chapitres 4–6, 1337, Hermann (1968) MR0240238
4 I V Cherednik, On the group-theoretical interpretation of Baker functions and τ–functions, Uspekhi Mat. Nauk 38 (1983) 133 MR728740
5 I Cherednik, Double affine Hecke algebras, 319, Cambridge Univ. Press (2005) MR2133033
6 I Cherednik, Jones polynomials of torus knots via DAHA, Int. Math. Res. Not. 2013 (2013) 5366 MR3142259
7 I Cherednik, DAHA-Jones polynomials of torus knots, Selecta Math. 22 (2016) 1013 MR3477341
8 I Cherednik, I Danilenko, DAHA and iterated torus knots, Algebr. Geom. Topol. 16 (2016) 843 MR3493410
9 I Cherednik, I Danilenko, DAHA approach to iterated torus links, from: "Categorification in geometry, topology, and physics" (editors A Beliakova, A D Lauda), Contemp. Math. 684, Amer. Math. Soc. (2017) 159 MR3611726
10 V Cherednik, R Elliot, Refined composite invariants of torus knots via DAHA, Ann. Fac. Sci. Toulouse Math. 25 (2016) 433 MR3530165
11 N M Dunfield, S Gukov, J Rasmussen, The superpolynomial for knot homologies, Experiment. Math. 15 (2006) 129 MR2253002
12 D Eisenbud, W Neumann, Three-dimensional link theory and invariants of plane curve singularities, 110, Princeton Univ. Press (1985) MR817982
13 P Etingof, E Gorsky, I Losev, Representations of rational Cherednik algebras with minimal support and torus knots, Adv. Math. 277 (2015) 124 MR3336085
14 H Fuji, S Gukov, P Sułkowski, Super-A–polynomial for knots and BPS states, Nuclear Phys. B 867 (2013) 506 MR2992793
15 M Goresky, R Kottwitz, R MacPherson, Purity of equivalued affine Springer fibers, Represent. Theory 10 (2006) 130 MR2209851
16 E Gorsky, q,t–Catalan numbers and knot homology, from: "Zeta functions in algebra and geometry" (editors A Campillo, G Cardona, A Melle-Hernández, W Veys), Contemp. Math. 566, Amer. Math. Soc. (2012) 213 MR2858925
17 E Gorsky, Arc spaces and DAHA representations, Selecta Math. 19 (2013) 125 MR3022754
18 E Gorsky, S Gukov, M Stosic, Quadruply-graded colored homology of knots, preprint (2013) arXiv:1304.3481
19 E Gorsky, M Mazin, Compactified Jacobians and q,t–Catalan numbers, I, J. Combin. Theory Ser. A 120 (2013) 49 MR2971696
20 E Gorsky, M Mazin, Compactified Jacobians and q,t–Catalan numbers, II, J. Algebraic Combin. 39 (2014) 153 MR3144397
21 E Gorsky, A Neguţ, Refined knot invariants and Hilbert schemes, J. Math. Pures Appl. 104 (2015) 403 MR3383172
22 E Gorsky, A Oblomkov, J Rasmussen, V Shende, Torus knots and the rational DAHA, Duke Math. J. 163 (2014) 2709 MR3273582
23 G M Greuel, G Pfister, Moduli spaces for torsion free modules on curve singularities,  I, J. Algebraic Geom. 2 (1993) 81 MR1185608
24 T Hausel, F Rodriguez-Villegas, Mixed Hodge polynomials of character varieties, Invent. Math. 174 (2008) 555 MR2453601
25 D Kazhdan, G Lusztig, Fixed point varieties on affine flag manifolds, Israel J. Math. 62 (1988) 129 MR947819
26 M Khovanov, Triply-graded link homology and Hochschild homology of Soergel bimodules, Internat. J. Math. 18 (2007) 869 MR2339573
27 M Khovanov, L Rozansky, Matrix factorizations and link homology, Fund. Math. 199 (2008) 1 MR2391017
28 M Khovanov, L Rozansky, Matrix factorizations and link homology, II, Geom. Topol. 12 (2008) 1387 MR2421131
29 G Laumon, Fibres de Springer et jacobiennes compactifiées, from: "Algebraic geometry and number theory" (editor V Ginzburg), Progr. Math. 253, Birkhäuser (2006) 515 MR2263199
30 G Lusztig, J M Smelt, Fixed point varieties on the space of lattices, Bull. London Math. Soc. 23 (1991) 213 MR1123328
31 D Maulik, Stable pairs and the HOMFLY polynomial, Invent. Math. 204 (2016) 787 MR3502065
32 D Maulik, Z Yun, Macdonald formula for curves with planar singularities, J. Reine Angew. Math. 694 (2014) 27 MR3259038
33 A Mellit, Toric braids and (m,n)–parking functions, preprint (2016) arXiv:1604.07456
34 L Migliorini, V Shende, A support theorem for Hilbert schemes of planar curves, J.  Eur. Math. Soc. 15 (2013) 2353 MR3120745
35 H R Morton, The coloured Jones function and Alexander polynomial for torus knots, Math. Proc. Cambridge Philos. Soc. 117 (1995) 129 MR1297899
36 A Oblomkov, J Rasmussen, V Shende, The Hilbert scheme of a plane curve singularity and the HOMFLY homology of its link, preprint (2012) arXiv:1201.2115
37 A Oblomkov, V Shende, The Hilbert scheme of a plane curve singularity and the HOMFLY polynomial of its link, Duke Math. J. 161 (2012) 1277 MR2922375
38 J Piontkowski, Topology of the compactified Jacobians of singular curves, Math. Z. 255 (2007) 195 MR2262728
39 J Rasmussen, Some differentials on Khovanov–Rozansky homology, Geom. Topol. 19 (2015) 3031 MR3447099
40 M Varagnolo, E Vasserot, Finite-dimensional representations of DAHA and affine Springer fibers : the spherical case, Duke Math. J. 147 (2009) 439 MR2510742
41 E Vasserot, Induced and simple modules of double affine Hecke algebras, Duke Math.  J. 126 (2005) 251 MR2115259
42 B Webster, G Williamson, A geometric construction of colored HOMFLYPT homology, Geom. Topol. 21 (2017) 2557 MR3687104
43 Z Yun, Global Springer theory, Adv. Math. 228 (2011) 266 MR2822234
44 Z Yun, Lectures on Springer theories and orbital integrals, preprint (2016) arXiv:1602.01451
45 O Zariski, Le problème des modules pour les branches planes, Hermann (1986) MR861277