Abstract
A family of new algebraic Poisson varieties will be constructed, generalising the complex character varieties of Riemann surfaces. Then the well-known (Poisson) mapping class group actions on the character varieties will be generalised.
-
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@incollection {ABM-purespinors, MRKEY = {2642360},
AUTHOR = {Alekseev, A. and Bursztyn, H. and Meinrenken, E.},
TITLE = {Pure spinors on {L}ie groups},
BOOKTITLE={From Probability to Geometry I. Volume in honor of the 60th birthday of Jean-Michel Bismut},
EDITOR={Dai, X. and Léandre, R. and Ma, X. and Zhang, W.},
SERIES = {Astérisque},
FJOURNAL = {Astérisque},
VOLUME = {327},
YEAR = {2009},
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ISSN = {0303-1179},
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} -
[cqv] P. P. Boalch, Global Weyl groups and a new theory of multiplicative quiver varieties, 2013.
@misc{cqv,
author = {Boalch, Philip P.},
TITLE = {Global {W}eyl groups and a new theory of multiplicative quiver varieties},
YEAR={2013},
ARXIV={1307.1033},
} -
[smapg]
P. P. Boalch, "Stokes matrices, Poisson Lie groups and Frobenius manifolds," Invent. Math., vol. 146, iss. 3, pp. 479-506, 2001.
@article {smapg, MRKEY = {1869848},
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JOURNAL = {Invent. Math.},
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YEAR = {2001},
NUMBER = {3},
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ISSN = {0020-9910},
CODEN = {INVMBH},
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MRNUMBER = {1869848},
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[smid]
P. P. Boalch, "Symplectic manifolds and isomonodromic deformations," Adv. Math., vol. 163, iss. 2, pp. 137-205, 2001.
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[bafi]
P. P. Boalch, "$G$-bundles, isomonodromy, and quantum Weyl groups," Int. Math. Res. Not., vol. 2002, p. no. 22, 1129-1166.
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[k2p]
P. P. Boalch, "From Klein to Painlevé via Fourier, Laplace and Jimbo," Proc. London Math. Soc., vol. 90, iss. 1, pp. 167-208, 2005.
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[saqh]
P. P. Boalch, "Quasi-Hamiltonian geometry of meromorphic connections," Duke Math. J., vol. 139, iss. 2, pp. 369-405, 2007.
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[iastalk07-nom] P. P. Boalch, Some geometry of irregular connections on curves, 2007.
@misc{iastalk07-nom,
author={Boalch, Philip P.},
TITLE = {Some geometry of irregular connections on curves},
NOTE={Talk at Workshop on Gauge Theory and Representation Theory, IAS Princeton, transparencies available on author's webpage},
YEAR={2007},
} -
[rsode] P. P. Boalch, Irregular connections and Kac–Moody root systems, 2008.
@misc{rsode,
author={Boalch, Philip P.},
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ARXIV={0806.1050},
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[fission]
P. P. Boalch, "Through the analytic halo: Fission via irregular singularities," Ann. Inst. Fourier $($Grenoble$)$, vol. 59, iss. 7, pp. 2669-2684, 2009.
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AUTHOR = {Boalch, Philip P.},
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JOURNAL = {Ann. Inst. Fourier $($Grenoble$)$},
FJOURNAL = {Université de Grenoble. Annales de l'Institut Fourier},
VOLUME = {59},
YEAR = {2009},
NUMBER = {7},
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CODEN = {AIFUA7},
MRCLASS = {53D30 (34M40)},
MRNUMBER = {2649336},
MRREVIEWER = {Andrei A. Kapaev},
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[logahoric]
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[slims]
P. P. Boalch, "Simply-laced isomonodromy systems," Publ. Math. I.H.E.S., vol. 116, pp. 1-68, 2012.
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JOURNAL={Publ. Math. I.H.E.S.},
VOLUME={116},
YEAR={2012},
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URL = {http://link.springer.com/article/10.1007/s10240-012-0044-8},
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[Dub95long]
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[Ugag]
M. Ugaglia, "On a Poisson structure on the space of Stokes matrices," Internat. Math. Res. Notices, iss. 9, pp. 473-493, 1999.
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JOURNAL = {Internat. Math. Res. Notices},
FJOURNAL = {International Mathematics Research Notices},
YEAR = {1999},
NUMBER = {9},
PAGES = {473--493},
ISSN = {1073-7928},
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MRNUMBER = {1692595},
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[vdb-doublepoisson]
M. Van den Bergh, "Double Poisson algebras," Trans. Amer. Math. Soc., vol. 360, iss. 11, pp. 5711-5769, 2008.
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JOURNAL = {Trans. Amer. Math. Soc.},
FJOURNAL = {Transactions of the American Mathematical Society},
VOLUME = {360},
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M. Van den Bergh, "Non-commutative quasi-Hamiltonian spaces," in Poisson Geometry in Mathematics and Physics, Providence, RI: Amer. Math. Soc., 2008, vol. 450, pp. 273-299.
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AUTHOR = {{Van den Bergh},
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TITLE = {Non-commutative quasi-{H}amiltonian spaces},
BOOKTITLE = {Poisson Geometry in Mathematics and Physics},
SERIES = {Contemp. Math.},
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PUBLISHER = {Amer. Math. Soc.},
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[Witten-wild]
E. Witten, "Gauge theory and wild ramification," Anal. Appl. $($Singap.$)$, vol. 6, iss. 4, pp. 429-501, 2008.
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[Woodh-sat]
N. M. J. Woodhouse, "The symplectic and twistor geometry of the general isomonodromic deformation problem," J. Geom. Phys., vol. 39, iss. 2, pp. 97-128, 2001.
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NUMBER = {2},
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[xu-poisson.inv]
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JOURNAL = {Ann. Sci. École Norm. Sup.},
FJOURNAL = {Annales Scientifiques de l'École Normale Supérieure. Quatrième Série},
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[yamakawa-mpa]
D. Yamakawa, "Geometry of multiplicative preprojective algebra," Int. Math. Res. Pap. IMRP, vol. 2008, p. I.
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TITLE = {Geometry of multiplicative preprojective algebra},
JOURNAL = {Int. Math. Res. Pap. IMRP},
FJOURNAL = {International Mathematics Research Papers. IMRP},
VOLUME = {2008},
PAGES = {Art. ID rpn008, 77pp},
ISSN = {1687-3017},
MRCLASS = {16G20 (14L30)},
MRNUMBER = {2470573},
ZBLNUMBER = {1197.16019},
DOI = {10.1093/imrp/rpn008},
}