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Non-orientable Surfaces from Lie Algebras

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Random Matrix Theory with an External Source

Part of the book series: SpringerBriefs in Mathematical Physics ((BRIEFSMAPHY,volume 19))

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Abstract

Usually Feyman diagrams related to real symmetric matrices are used for generating non-orientable surfaces. The Euler characteristics of non-orientable surfaces have been derived from real symmetric matrices (Goulden et al., Trans Amer Math Soc 353:4405–4427, 2001, [68]). There are also studies of integrable systems which satisfies the Drinfeld–Sokolov hierarchy (Drinfeld and Sokolov, J Math Sci 30:1975–2036, 1985, [56]), and they are related to non-orientable surfaces (Bertola et al., Simple lie algebras and topological ODEs; Fan et al., Annals of Math 178:1–106, 2013, [47, 59]).

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Correspondence to Edouard Brézin .

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Brézin, E., Hikami, S. (2016). Non-orientable Surfaces from Lie Algebras. In: Random Matrix Theory with an External Source. SpringerBriefs in Mathematical Physics, vol 19. Springer, Singapore. https://doi.org/10.1007/978-981-10-3316-2_9

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