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Symmetry, Integrability and Geometry: Methods and Applications, 2017, Volume 13, 052, 28 pp.
DOI: https://doi.org/10.3842/SIGMA.2017.052 (Mi sigma1252) 		 
This article is cited in 8 scientific papers (total in 8 papers)

A Combinatorial Study on Quiver Varieties

Shigeyuki Fujiia, Satoshi Minabeb

a Accenture Strategy, 107-8672 Tokyo, Japan
b Department of Mathematics, Tokyo Denki University, 120-8551 Tokyo, Japan
Full-text PDF (611 kB) Citations (8)
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DOI: https://doi.org/10.3842/SIGMA.2017.052
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.
Keywords: Young diagram; core; quotient; quiver variety; instanton.
Funding agency Grant number
Nagoya University
Japan Society for the Promotion of Science JP17K05228
Sumitomo Foundation
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.
Received: January 13, 2017; in final form June 30, 2017; Published online July 6, 2017
Bibliographic databases:
Document Type: Article
MSC: 14C05; 14D21; 05A19; 05E10
Language: English
Citation: Shigeyuki Fujii, Satoshi Minabe, “A Combinatorial Study on Quiver Varieties”, SIGMA, 13 (2017), 052, 28 pp.
Citation in format AMSBIB
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    • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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