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Quiver Varieties with Multiplicities, Weyl Groups of Non-Symmetric Kac-Moody Algebras, and Painlevé Equations

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dc.contributor.author Yamakawa, D.
dc.date.accessioned 2019-02-09T19:50:03Z
dc.date.available 2019-02-09T19:50:03Z
dc.date.issued 2010
dc.identifier.citation Quiver Varieties with Multiplicities, Weyl Groups of Non-Symmetric Kac-Moody Algebras, and Painlevé Equations / D. Yamakawa // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 31 назв. — англ. uk_UA
dc.identifier.issn 1815-0659
dc.identifier.other 2010 Mathematics Subject Classification: 53D30; 16G20; 20F55; 34M55
dc.identifier.other DOI:10.3842/SIGMA.2010.087
dc.identifier.uri http://dspace.nbuv.gov.ua/handle/123456789/146522
dc.description.abstract To a finite quiver equipped with a positive integer on each of its vertices, we associate a holomorphic symplectic manifold having some parameters. This coincides with Nakajima's quiver variety with no stability parameter/framing if the integers attached on the vertices are all equal to one. The construction of reflection functors for quiver varieties are generalized to our case, in which these relate to simple reflections in the Weyl group of some symmetrizable, possibly non-symmetric Kac-Moody algebra. The moduli spaces of meromorphic connections on the rank 2 trivial bundle over the Riemann sphere are described as our manifolds. In our picture, the list of Dynkin diagrams for Painlevé equations is slightly different from (but equivalent to) Okamoto's uk_UA
dc.description.sponsorship I am grateful to Philip Boalch for stimulating conversations, and to Professor Hiraku Nakajima for valuable comments. This work was supported by the grants ANR-08-BLAN-0317-01 of the Agence nationale de la recherche and JSPS Grant-in-Aid for Scientific Research (S 19104002). uk_UA
dc.language.iso en uk_UA
dc.publisher Інститут математики НАН України uk_UA
dc.relation.ispartof Symmetry, Integrability and Geometry: Methods and Applications
dc.title Quiver Varieties with Multiplicities, Weyl Groups of Non-Symmetric Kac-Moody Algebras, and Painlevé Equations uk_UA
dc.type Article uk_UA
dc.status published earlier uk_UA


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