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We study the Andrews-Gordon-Bressoud (AGB) generalisations of the Rogers-Ramanujan q-series identities in the context of cylindric partitions.
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P Paule, The concept of Bailey chains , Séminaire Lotharingien de Combinatoire 18f
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A Berkovich and B M McCoy, Generalizations of the Andrews-Bressoud identities for the N = 1 N\!=\!1 superconformal model S M ( 2 , 4 ν ) SM(2,4\nu)
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M Jimbo, T Miwa and M Okado, Local state probabilities of solvable lattice models: An A 1 ( 1 ) A^{(1)}_{1} family , Nuclear Physics B300
1988
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D M Bressoud, Lattice paths and the Rogers-Ramanujan identities in ‘Proceedings of the international Ramanujan centenary conference, 1987 Madras’, K Alladi, Editor, Lecture Notes in Mathematics 1395
1989
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E Date, M Jimbo, A Kuniba, T Miwa and M Okado, Paths, Maya diagrams, and representations of 𝔰 𝔩 ^ ( r , C ) \widehat{\mathfrak{sl}}(r,C) , Advanced Studies in Pure Mathematics 19
1989
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V Kac, Infinite Dimensional Lie algebras , 3rd edition, Cambridge University Press, Cambridge, UK, 1990
1990
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V A Fateev and S L Lukyanov, The models of two-dimensional conformal quantum field theory with ℤ N {\mathbb{Z}}_{N} symmetry . International Journal of Modern Physics A3
1990
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T Nakanishi, Non-unitary minimal models and RSOS models , Nuclear Physics B334
1990
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M Jimbo, K Misra, T Miwa and M Okado, Combinatorics of representations of U q ( s l ( n ) ^ ) U_{q}(\widehat{sl(n)}) at q = 0 q=0 , Communications in Mathematical Physics 136
1991
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A Berkovich, B M McCoy and A Schilling, Rogers-Schur-Ramanujan-type identities for the M ( p , p ′ ) M(p,p^{\prime}) minimal models of conformal field theory
1998
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G E Andrews, A Schilling and S O Warnaar, An A 2 Bailey lemma and Rogers–Ramanujan-type identities , Journal of the American Mathematical Society 12
1999
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O Foda, B Leclerc, M Okado, J-Y Thibon and T A Welsh, Branching functions of A n − 1 ( 1 ) A_{n-1}^{(1)} and Jantzen-Seitz problem for Ariki-Koike algebras , Advances in Mathematics 141
1999
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T Miwa, M Jimbo and E Date, Solitons: Differential equations, symmetries and infinite dimensional algebras
2000
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2000
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2005
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A Borodin, Periodic Schur process and cylindric partitions
2007
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B Feigin, O Foda and T Welsh, Andrews-Gordon identities from combinations of Virasoro characters , Ramanujan Journal 17
2008
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Ch Krattenthaler, Alternative proof of a proposition on cylindric partitions by Alexei Borodin
2008
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P Tingley, Three combinatorial models for 𝔰 𝔩 ^ n \widehat{\mathfrak{sl}}_{n} crystals, with applications to cylindric plane partitions , Mathematical Research Notices IMRN 2008, arXiv:math/0702062
2008
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O Blondeau-Fournier, P Mathieu and T A Welsh, Half-lattice paths and Virasoro characters
2012
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K B Alkalaev and V A Belavin, Conformal blocks of W N W_{N} Minimal Models and AGT correspondence
2014
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M Bershtein and O Foda, AGT, Burge pairs and minimal models
2014
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O Foda and J-F Wu, From topological strings to minimal models
2015
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S O Warnaar, 50 years of Bailey’s lemma
2062
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