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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2011, Volume 275, Pages 295–300 (Mi tm3351)  
Hecke graphs, Ramanujan graphs and generalized duality transformations for lattice spin systems

M. I. Monastyrsky

Institute for Theoretical and Experimental Physics, Moscow, Russia
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Abstract: I discuss two related subjects: (1) Hecke surfaces and $k$-regular graphs, (2) duality transformations for lattice spin models. Each of them is related to deep mathematical and physical theories, and at first glance, they have nothing in common. However, it became evident in recent years that there exist deep internal relations between these two problems. Especially interesting (and mysterious) is the role of Hecke groups in this context. I consider the following relevant example: Hecke graphs and Ramanujan graphs.
Received in May 2011
English version:
Proceedings of the Steklov Institute of Mathematics, 2011, Volume 275, Pages 284–289
DOI: https://doi.org/10.1134/S0081543811080190
Bibliographic databases:
Document Type: Article
UDC: 519.17
Language: English
Citation: M. I. Monastyrsky, “Hecke graphs, Ramanujan graphs and generalized duality transformations for lattice spin systems”, Classical and modern mathematics in the wake of Boris Nikolaevich Delone, Collected papers. In commemoration of the 120th anniversary of Boris Nikolaevich Delone's birth, Trudy Mat. Inst. Steklova, 275, MAIK Nauka/Interperiodica, Moscow, 2011, 295–300; Proc. Steklov Inst. Math., 275 (2011), 284–289
Citation in format AMSBIB
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\paper Hecke graphs, Ramanujan graphs and generalized duality transformations for lattice spin systems
\inbook Classical and modern mathematics in the wake of Boris Nikolaevich Delone
\bookinfo Collected papers. In commemoration of the 120th anniversary of Boris Nikolaevich Delone's birth
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\yr 2011
\vol 275
\pages 295--300
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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