Geometry & Topology Volume 19, issue 6 (2015)

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the journal

Ethics and policies

Peer-review process

Submission guidelines

Submission form

Editorial board

Subscriptions

ISSN (electronic): 1364-0380

ISSN (print): 1465-3060

Author index

To appear

Other MSP journals

Global Weyl groups and a new theory of multiplicative quiver varieties

Philip Boalch

Geometry & Topology 19 (2015) 3467–3536

DOI: 10.2140/gt.2015.19.3467

Bibliography

1	M R Adams, J Harnad, J Hurtubise, Dual moment maps into loop algebras, Lett. Math. Phys. 20 (1990) 299 MR1077962
2	A Alekseev, A Malkin, E Meinrenken, Lie group valued moment maps, J. Differential Geom. 48 (1998) 445 MR1638045
3	D Arinkin, S Lysenko, Isomorphisms between moduli spaces of $\mathrm{SL}(2)$–bundles with connections on $\mathbf{P}^1\setminus \{x_1,\ldots, x_4\}$, Math. Res. Lett. 4 (1997) 181 MR1453052
4	M F Atiyah, R Bott, The Yang–Mills equations over Riemann surfaces, Philos. Trans. Roy. Soc. London Ser. A 308 (1983) 523 MR702806
5	M F Atiyah, V G Drinfel’d, N J Hitchin, Y I Manin, Construction of instantons, Phys. Lett. A 65 (1978) 185 MR598562
6	W Balser, W B Jurkat, D A Lutz, On the reduction of connection problems for differential equations with an irregular singular point to ones with only regular singularities, I, SIAM J. Math. Anal. 12 (1981) 691 MR625827
7	M Van den Bergh, Double Poisson algebras, Trans. Amer. Math. Soc. 360 (2008) 5711 MR2425689
8	M Van den Bergh, Non-commutative quasi-Hamiltonian spaces, from: "Poisson geometry in mathematics and physics" (editors G Dito, J H Lu, Y Maeda, A Weinstein), Contemp. Math. 450, Amer. Math. Soc. (2008) 273 MR2397630
9	O Biquard, P P Boalch, Wild non-abelian Hodge theory on curves, Compos. Math. 140 (2004) 179 MR2004129
10	P P Boalch, Irregular connections and Kac–Moody root systems, arXiv:0806.1050
11	P P Boalch, Symplectic geometry and isomonodromic deformations, PhD thesis, Oxford University (1999)
12	P P Boalch, Symplectic manifolds and isomonodromic deformations, Adv. Math. 163 (2001) 137 MR1864833
13	P P Boalch, Quasi-Hamiltonian geometry of meromorphic connections, preprint (2002) arXiv:math/0203161
14	P P Boalch, Painlevé equations and complex reflections, from: "Proceedings of the International Conference in Honor of Frédéric Pham", Ann. Inst. Fourier 53 (2003) 1009 MR2033508
15	P P Boalch, From Klein to Painlevé via Fourier, Laplace and Jimbo, Proc. London Math. Soc. 90 (2005) 167 MR2107041
16	P P Boalch, Quasi-Hamiltonian geometry of meromorphic connections, Duke Math. J. 139 (2007) 369 MR2352135
17	P P Boalch, Some geometry of irregular connections on curves (2007)
18	P P Boalch, Irregular connections, Hitchin systems and Kac–Moody root systems (2009)
19	P P Boalch, Quivers and difference Painlevé equations, from: "Groups and symmetries" (editors J Harnad, P Winternitz), CRM Proc. Lecture Notes 47, Amer. Math. Soc. (2009) 25 MR2500553
20	P P Boalch, Through the analytic halo: Fission via irregular singularities, Ann. Inst. Fourier (Grenoble) 59 (2009) 2669 MR2649336
21	P P Boalch, Riemann–Hilbert for tame complex parahoric connections, Transform. Groups 16 (2011) 27 MR2785493
22	P P Boalch, Geometry of moduli spaces of meromorphic connections on curves, Stokes data, wild nonabelian Hodge theory, hyperkähler manifolds, isomonodromic deformations, Painlevé equations, and relations to Lie theory, Habilitation memoir, Université Paris-Sud (2012)
23	P P Boalch, Hyperkähler manifolds and nonabelian Hodge theory of (irregular) curves (2012)
24	P P Boalch, Simply-laced isomonodromy systems, Publ. Math. Inst. Hautes Études Sci. 116 (2012) 1 MR3090254
25	P P Boalch, Geometry and braiding of Stokes data; fission and wild character varieties, Ann. of Math. 179 (2014) 301 MR3126570
26	W Crawley-Boevey, On matrices in prescribed conjugacy classes with no common invariant subspace and sum zero, Duke Math. J. 118 (2003) 339 MR1980997
27	W Crawley-Boevey, Indecomposable parabolic bundles and the existence of matrices in prescribed conjugacy class closures with product equal to the identity, Publ. Math. Inst. Hautes Études Sci. (2004) 171 MR2102700
28	W Crawley-Boevey, Quiver algebras, weighted projective lines, and the Deligne–Simpson problem, from: "International Congress of Mathematicians, II" (editors M Sanz-Solé, J Soria, J L Varona, J Verdera), Eur. Math. Soc. (2006) 117 MR2275591
29	W Crawley-Boevey, M P Holland, Noncommutative deformations of Kleinian singularities, Duke Math. J. 92 (1998) 605 MR1620538
30	W Crawley-Boevey, P Shaw, Multiplicative preprojective algebras, middle convolution and the Deligne–Simpson problem, Adv. Math. 201 (2006) 180 MR2204754
31	P Deligne, Équations différentielles à points singuliers réguliers, Lecture Notes in Mathematics 163, Springer (1970) MR0417174
32	M Dettweiler, S Reiter, An algorithm of Katz and its application to the inverse Galois problem, J. Symbolic Comput. 30 (2000) 761 MR1800678
33	P Etingof, A Oblomkov, E Rains, Generalized double affine Hecke algebras of rank 1 and quantized del Pezzo surfaces, Adv. Math. 212 (2007) 749 MR2329319
34	M Groechenig, Hilbert schemes as moduli of Higgs bundles and local systems, Int. Math. Res. Not. 2014 (2014) 6523
35	J Harnad, Dual isomonodromic deformations and moment maps to loop algebras, Comm. Math. Phys. 166 (1994) 337 MR1309553
36	K Hiroe, D Yamakawa, Moduli spaces of meromorphic connections and quiver varieties, Adv. Math. 266 (2014) 120
37	N J Hitchin, The self-duality equations on a Riemann surface, Proc. London Math. Soc. 55 (1987) 59 MR887284
38	N J Hitchin, Frobenius manifolds, from: "Gauge theory and symplectic geometry" (editors J Hurtubise, F Lalonde), NATO Advanced Science Institutes Series C: Mathematical and Physical Sciences 488, Kluwer (1997) 69 MR1461567
39	V G Kac, Infinite-dimensional Lie algebras, Cambridge Univ. Press (1990) MR1104219
40	N M Katz, Rigid local systems, Annals of Mathematics Studies 139, Princeton Univ. Press (1996) MR1366651
41	A D King, Moduli of representations of finite-dimensional algebras, Quart. J. Math. Oxford Ser. 45 (1994) 515 MR1315461
42	V P Kostov, On the Deligne–Simpson problem, C. R. Acad. Sci. Paris Sér. I Math. 329 (1999) 657 MR1724102
43	V P Kostov, Additive Deligne–Simpson problem for non-Fuchsian systems, Funkcial. Ekvac. 53 (2010) 395 MR2761090
44	H Kraft, C Procesi, Closures of conjugacy classes of matrices are normal, Invent. Math. 53 (1979) 227 MR549399
45	P B Kronheimer, The construction of ALE spaces as hyper-Kähler quotients, J. Differential Geom. 29 (1989) 665 MR992334
46	P B Kronheimer, H Nakajima, Yang–Mills instantons on ALE gravitational instantons, Math. Ann. 288 (1990) 263 MR1075769
47	B Malgrange, Équations différentielles à coefficients polynomiaux, Progress in Mathematics 96, Birkhäuser (1991) MR1117227
48	H Nakajima, Instantons on ALE spaces, quiver varieties, and Kac–Moody algebras, Duke Math. J. 76 (1994) 365 MR1302318
49	H Nakajima, Quiver varieties and Kac–Moody algebras, Duke Math. J. 91 (1998) 515 MR1604167
50	H Nakajima, Quiver varieties and quantum affine algebras, Sugaku Expositions 19 (2006) 53 MR2215055
51	A Pressley, G Segal, Loop groups, Oxford University Press (1986) MR900587
52	C Sabbah, Harmonic metrics and connections with irregular singularities, Ann. Inst. Fourier (Grenoble) 49 (1999) 1265 MR1703088
53	C T Simpson, Harmonic bundles on noncompact curves, J. Amer. Math. Soc. 3 (1990) 713 MR1040197
54	C T Simpson, Products of matrices, from: "Differential geometry, global analysis, and topology" (editors A Nicas, W F Shadwick), CMS Conf. Proc. 12, Amer. Math. Soc. (1991) 157 MR1158474
55	C T Simpson, Katz's middle convolution algorithm, Pure Appl. Math. Q. 5 (2009) 781 MR2508903
56	S Szabó, Nahm transform for integrable connections on the Riemann sphere, Mém. Soc. Math. Fr. 110 (2007) MR2482471
57	D Yamakawa, Geometry of multiplicative preprojective algebra, Int. Math. Res. Pap. (2008) MR2470573