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Russian Mathematical Surveys, 2015, Volume 70, Issue 4, Pages 715–773
DOI: https://doi.org/10.1070/RM2015v070n04ABEH004958 (Mi rm9667) 		 
This article is cited in 11 scientific papers (total in 11 papers)

Infinite symmetric groups and combinatorial constructions of topological field theory type

Yu. A. Neretinabcd

a University of Vienna, Vienna, Austria
b Institute for Theoretical and Experimental Physics, Moscow
c Moscow State University
d Institute for Information Transmission Problems, Russian Academy of Sciences
English version PDF (1156 kB) Citations (11)
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DOI: https://doi.org/10.1070/RM2015v070n04ABEH004958
Abstract: This paper contains a survey of train constructions for infinite symmetric groups and related groups. For certain pairs (a group $G$, a subgroup $K$) categories are constructed whose morphisms are two-dimensional surfaces tiled by polygons and coloured in a certain way. A product of morphisms is a gluing together of combinatorial bordisms, and functors from the category of bordisms to the category of Hilbert spaces and bounded operators correspond to unitary representations of $G$. The construction has numerous variations: instead of surfaces there can also be one-dimensional objects of Brauer diagram type, multidimensional pseudomanifolds, and bipartite graphs.
Bibliography: 66 titles.
Keywords: infinite symmetric group, representations of categories, spherical representations, double cosets, bordisms.
Funding agency Grant number
Austrian Science Fund P25142
This work was supported by the Austrian Science Fund FWF (grant no. P25142).
Received: 01.12.2014
Russian version:
Uspekhi Matematicheskikh Nauk, 2015, Volume 70, Issue 4(424), Pages 143–204
DOI: https://doi.org/10.4213/rm9667
Bibliographic databases:
Document Type: Article
UDC: 517.986.4+519.12+512.583
MSC: 20B30, 20C32
Language: English
Original paper language: Russian
Citation: Yu. A. Neretin, “Infinite symmetric groups and combinatorial constructions of topological field theory type”, Uspekhi Mat. Nauk, 70:4(424) (2015), 143–204; Russian Math. Surveys, 70:4 (2015), 715–773
Citation in format AMSBIB
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    • This publication is cited in the following 11 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Russian version PDF:451
    English version PDF:26
    References:92
    First page:70
     
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