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We study a quantum (non-commutative) representation of the affine Weyl group mainly of type $E_8^{(1)}$, where the representation is given by birational actions on two variables $x$, $y$ with $q$-commutation relations.
1903
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1905
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2016
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Hasegawa K., Quantizing the Bäcklund transformations of Painlevé equations and the quantum discrete Painlevé VI equation, in Exploring New Structures and Natural Constructions in Mathematical Physics,
2011
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Gamayun O., Iorgov N., Lisovyy O., Conformal field theory of Painlevé VI,
2012
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Huang M.-X., On gauge theory and topological string in Nekrasov–Shatashvili limit,
2012
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Hatsuda Y., Moriyama S., Okuyama K., Instanton effects in ABJM theory from Fermi gas approach,
2013
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Hatsuda Y., Moriyama S., Okuyama K., Instanton bound states in ABJM theory,
2013
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2017
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Jimbo M., Nagoya H., Sakai H., CFT approach to the
2017
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Kajiwara K., Noumi M., Yamada Y., Geometric aspects of Painlevé equations,
2017
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Moriyama S., Nosaka T., Yano K., Superconformal Chern–Simons theories from del Pezzo geometries,
2017
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Yamada Y., An elliptic Garnier system from interpolation,
2017
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Bershtein M., Gavrylenko P., Marshakov A., Cluster integrable systems,
2018
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2018
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2020
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Kels A.P., Yamazaki M., Lens generalisation of
2021
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