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Izv. RAN. Ser. Mat., 2008, Volume 72, Issue 4, Pages 3–24 (Mi izv737)  

This article is cited in 12 scientific papers (total in 12 papers)

The algebra of bipartite graphs and Hurwitz numbers of seamed surfaces

A. V. Alekseevskiia, S. M. Natanzonbca

a A. N. Belozersky Institute of Physico-Chemical Biology, M. V. Lomonosov Moscow State University
b Institute for Theoretical and Experimental Physics (Russian Federation State Scientific Center)
c Independent University of Moscow

Abstract: We extend the definition of Hurwitz numbers to the case of seamed surfaces, which arise in new models of mathematical physics, and prove that they form a system of correlators for a Klein topological field theory in the sense defined in [1]. We find the corresponding Cardy–Frobenius algebras, which yield a method for calculating the Hurwitz numbers. As a by-product, we prove that the vector space generated by the bipartite graphs with $n$ edges possesses a natural binary operation that makes this space into a non-commutative Frobenius algebra isomorphic to the algebra of intertwining operators for a representation of the symmetric group $S_n$ on the space generated by the set of all partitions of a set of $n$ elements.

DOI: https://doi.org/10.4213/im737

Full text: PDF file (593 kB)
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English version:
Izvestiya: Mathematics, 2008, 72:4, 627–646

Bibliographic databases:

UDC: 514.7+512.7
MSC: 30F50, 14H30, 20C05, 81T45
Received: 28.12.2005
Revised: 15.02.2007

Citation: A. V. Alekseevskii, S. M. Natanzon, “The algebra of bipartite graphs and Hurwitz numbers of seamed surfaces”, Izv. RAN. Ser. Mat., 72:4 (2008), 3–24; Izv. Math., 72:4 (2008), 627–646

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. Yu. Morozov, “Unitary integrals and related matrix models”, Theoret. and Math. Phys., 162:1 (2010), 1–33  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    2. Natanzon S.M., “Cyclic foam topological field theories”, J. Geom. Phys., 60:6-8 (2010), 874–883  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    3. A. D. Mironov, A. Yu. Morozov, S. M. Natanzon, “Complete set of cut-and-join operators in the Hurwitz–Kontsevich theory”, Theoret. and Math. Phys., 166:1 (2011), 1–22  mathnet  crossref  crossref  mathscinet  adsnasa  isi
    4. Sergey A. Loktev, Sergey M. Natanzon, “Klein Topological Field Theories from Group Representations”, SIGMA, 7 (2011), 070, 15 pp.  mathnet  crossref  mathscinet
    5. Costa A.F., Gusein-Zade S.M., Natanzon S.M., “Klein Foams”, Indiana Univ. Math. J., 60:3 (2011), 985–995  crossref  mathscinet  isi  elib  scopus
    6. Mironov A., Morozov A., Natanzon S., “Algebra of differential operators associated with Young diagrams”, J. Geom. Phys., 62:2 (2012), 148–155  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    7. Andrey Mironov, Aleksey Morozov, Sergey Natanzon, “Infinite-dimensional topological field theories from Hurwitz numbers”, J. Knot Theory Ramifications, 23:06 (2014), 1450033  crossref  mathscinet  zmath  scopus
    8. A. Yu. Orlov, “Hurwitz numbers and products of random matrices”, Theoret. and Math. Phys., 192:3 (2017), 1282–1323  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    9. Natanzon S.M., Orlov A.Yu., “BKP and Projective Hurwitz Numbers”, Lett. Math. Phys., 107:6 (2017), 1065–1109  crossref  mathscinet  zmath  isi  scopus
    10. Gusein-Zade S.M., Natanzon S.M., “Klein Foams as Families of Real Forms of Riemann Surfaces”, Adv. Theor. Math. Phys., 21:1 (2017), 231–241  crossref  mathscinet  zmath  isi  scopus
    11. Mironov A., Morozov A., Natanzon S., “Cut-and-Join Structure and Integrability For Spin Hurwitz Numbers”, Eur. Phys. J. C, 80:2 (2020), 97  crossref  isi
    12. S. M. Natanzon, A. Yu. Orlov, “Hurwitz numbers from Feynman diagrams”, Theoret. and Math. Phys., 204:3 (2020), 1166–1194  mathnet  crossref  crossref  isi  elib
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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