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A Combinatorial Study on Quiver Varieties
Репозиторій DSpace/Manakin
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- Фізико-технічні та математичні науки
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- Відділення математики
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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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A Combinatorial Study on Quiver Varieties
Інший ID:
2010 Mathematics Subject Classification: 14C05; 14D21; 05A19; 05E10
DOI:10.3842/SIGMA.2017.052
DOI:10.3842/SIGMA.2017.052
Посилання:
A Combinatorial Study on Quiver Varieties / S. Fujii, S. Minabe // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 58 назв. — англ.
Підтримка:
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.
Дата:
2017
Переглядів:
647
Завантажень:
270
Анотація:
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.
