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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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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DOI: https://doi.org/10.1007/978-981-10-3316-2_9
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