A Combinatorial Study on Quiver Varieties
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....
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2017 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2017
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/148584 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | A Combinatorial Study on Quiver Varieties / S. Fujii, S. Minabe // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 58 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862656017651728384 |
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| author | Fujii, S. Minabe, S. |
| author_facet | Fujii, S. Minabe, S. |
| citation_txt | A Combinatorial Study on Quiver Varieties / S. Fujii, S. Minabe // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 58 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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.
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| first_indexed | 2025-12-02T03:30:16Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-148584 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-02T03:30:16Z |
| publishDate | 2017 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Fujii, S. Minabe, S. 2019-02-18T16:15:12Z 2019-02-18T16:15:12Z 2017 A Combinatorial Study on Quiver Varieties / S. Fujii, S. Minabe // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 58 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 14C05; 14D21; 05A19; 05E10 DOI:10.3842/SIGMA.2017.052 https://nasplib.isofts.kiev.ua/handle/123456789/148584 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. 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. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications A Combinatorial Study on Quiver Varieties Article published earlier |
| spellingShingle | A Combinatorial Study on Quiver Varieties Fujii, S. Minabe, S. |
| title | A Combinatorial Study on Quiver Varieties |
| title_full | A Combinatorial Study on Quiver Varieties |
| title_fullStr | A Combinatorial Study on Quiver Varieties |
| title_full_unstemmed | A Combinatorial Study on Quiver Varieties |
| title_short | A Combinatorial Study on Quiver Varieties |
| title_sort | combinatorial study on quiver varieties |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/148584 |
| work_keys_str_mv | AT fujiis acombinatorialstudyonquivervarieties AT minabes acombinatorialstudyonquivervarieties AT fujiis combinatorialstudyonquivervarieties AT minabes combinatorialstudyonquivervarieties |