A Combinatorial Study on Quiver Varieties

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Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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Symmetry, Integrability and Geometry: Methods and Applications, 2017, том 13
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Symmetry, Integrability and Geometry: Methods and Applications, 2017, том 13, випуск за цей рік
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dc.contributor.author	Fujii, S.
dc.contributor.author	Minabe, S.
dc.date.accessioned	2019-02-18T16:15:12Z
dc.date.available	2019-02-18T16:15:12Z
dc.date.issued	2017
dc.identifier.citation	A Combinatorial Study on Quiver Varieties / S. Fujii, S. Minabe // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 58 назв. — англ.	uk_UA
dc.identifier.issn	1815-0659
dc.identifier.other	2010 Mathematics Subject Classification: 14C05; 14D21; 05A19; 05E10
dc.identifier.other	DOI:10.3842/SIGMA.2017.052
dc.identifier.uri	http://dspace.nbuv.gov.ua/handle/123456789/148584
dc.description.abstract	This is an expository paper which has two parts. In the first part, we study quiver varieties of affine A-type from a combinatorial point of view. We present a combinatorial method for obtaining a closed formula for the generating function of Poincaré polynomials of quiver varieties in rank 1 cases. Our main tools are cores and quotients of Young diagrams. In the second part, we give a brief survey of instanton counting in physics, where quiver varieties appear as moduli spaces of instantons, focusing on its combinatorial aspects.	uk_UA
dc.description.sponsorship	The authors would like to thank H. Awata, H. Miyachi, W. Nakai, H. Nakajima, T. Nakatsu, M. Namba, Y. Nohara, Y. Hashimoto, Y. Ito, T. Sasaki, Y. Tachikawa, K. Takasaki, and K. Ueda for valuable discussions and comments. The authors express their deep gratitudes to M. Hamanaka, S. Moriyama, and A. Tsuchiya for their advices and warm encouragements, and especially to H. Kanno for suggesting a problem and reading the manuscript carefully. This work was started while the authors enjoyed the hospitality of the Fields Institute at University of Toronto on the fall of 2004. The authors are grateful to K. Hori for invitation. Throughout this work, the authors’ research was supported in part by COE program in mathematics at Nagoya University. Added in 2017. The authors thank the referees for useful comments. During the revision in 2017, S.M. is supported in part by Grant for Basic Science Research Projects from the Sumitomo Foundation and JSPS KAKENHI Grand number JP17K05228.	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	A Combinatorial Study on Quiver Varieties	uk_UA
dc.type	Article	uk_UA
dc.status	published earlier	uk_UA