Аннотация:
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.
Ключевые слова:
Young diagram; core; quotient; quiver variety; instanton.
Throughout this work, the authors’ research was supported in part by COE program in mathematics at Nagoya University.
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.
Поступила:13 января 2017 г.; в окончательном варианте 30 июня 2017 г.; опубликована 6 июля 2017 г.
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\by Shigeyuki~Fujii, Satoshi~Minabe
\paper A Combinatorial Study on Quiver Varieties
\jour SIGMA
\yr 2017
\vol 13
\papernumber 052
\totalpages 28
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\crossref{https://doi.org/10.3842/SIGMA.2017.052}
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Эта публикация цитируется в следующих 8 статьяx:
Taro Kimura, “Double Quiver Gauge Theory and BPS/CFT Correspondence”, SIGMA, 19 (2023), 039, 32 pp.
Mikhail Bershtein, Roman Gonin, “Twisted Representations of Algebra of q-Difference Operators, Twisted q-W Algebras and Conformal Blocks”, SIGMA, 16 (2020), 077, 55 pp.
B. Davison, J. Ongaro, B. Szendroi, “Enumerating coloured partitions in 2 and 3 dimensions”, Math. Proc. Camb. Philos. Soc., 169:3 (2020), 479–505
M. Manabe, “N-th parafermion wn characters from U(N) instanton counting on C-2/Z(N)”, J. High Energy Phys., 2020, no. 6, 112
O. Foda, N. Macleod, M. Manabe, T. Welsh, “(sl)over-cap(n) wzw conformal blocks from su (N) instanton partition functions on C-2/Z(N)”, Nucl. Phys. B, 956 (2020), 115038
H. Awata, H. Kanno, A. Mironov, A. Morozov, K. Suetake, Y. Zenkevich, “(q,t)-KZ equations for quantum toroidal algebra and Nekrasov partition functions on ALE spaces”, J. High Energy Phys., 2018, no. 3, 192
T. D. Brennan, A. Dey, G. W. Moore, “On ’t Hooft defects, monopole bubbling and supersymmetric quantum mechanics”, J. High Energy Phys., 2018, no. 9, 014
Ádám Gyenge, András Némethi, Balázs Szendrői, “Euler characteristics of Hilbert schemes of points on simple surface singularities”, European Journal of Mathematics, 4:2 (2018), 439
Цитирование в формате AMSBIB
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