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Title: Generalized zeta function representation of groups and 2-dimensional topological Yang-Mills theory: The example of GL(2, #Mathematical Double-Struck Capital F#{sub q}) and PGL(2, #Mathematical Double-Struck Capital F#{sub q})

Abstract

We recall the relation between zeta function representation of groups and two-dimensional topological Yang-Mills theory through Mednikh formula. We prove various generalisations of Mednikh formulas and define generalization of zeta function representations of groups. We compute some of these functions in the case of the finite group GL(2, #Mathematical Double-Struck Capital F#{sub q}) and PGL(2, #Mathematical Double-Struck Capital F#{sub q}). We recall the table characters of these groups for any q, compute the Frobenius-Schur indicator of their irreducible representations, and give the explicit structure of their fusion rings.

Authors:
 [1]
  1. Université Montpellier 2, CNRS, L2C, IMAG, Montpellier (France)
Publication Date:
OSTI Identifier:
22597042
Resource Type:
Journal Article
Journal Name:
Journal of Mathematical Physics
Additional Journal Information:
Journal Volume: 57; Journal Issue: 3; Other Information: (c) 2016 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0022-2488
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; IRREDUCIBLE REPRESENTATIONS; TOPOLOGY; TWO-DIMENSIONAL CALCULATIONS; YANG-MILLS THEORY

Citation Formats

Roche, Ph., E-mail: philippe.roche@univ-montp2.fr. Generalized zeta function representation of groups and 2-dimensional topological Yang-Mills theory: The example of GL(2, #Mathematical Double-Struck Capital F#{sub q}) and PGL(2, #Mathematical Double-Struck Capital F#{sub q}). United States: N. p., 2016. Web. doi:10.1063/1.4943294.
Roche, Ph., E-mail: philippe.roche@univ-montp2.fr. Generalized zeta function representation of groups and 2-dimensional topological Yang-Mills theory: The example of GL(2, #Mathematical Double-Struck Capital F#{sub q}) and PGL(2, #Mathematical Double-Struck Capital F#{sub q}). United States. https://doi.org/10.1063/1.4943294
Roche, Ph., E-mail: philippe.roche@univ-montp2.fr. 2016. "Generalized zeta function representation of groups and 2-dimensional topological Yang-Mills theory: The example of GL(2, #Mathematical Double-Struck Capital F#{sub q}) and PGL(2, #Mathematical Double-Struck Capital F#{sub q})". United States. https://doi.org/10.1063/1.4943294.
@article{osti_22597042,
title = {Generalized zeta function representation of groups and 2-dimensional topological Yang-Mills theory: The example of GL(2, #Mathematical Double-Struck Capital F#{sub q}) and PGL(2, #Mathematical Double-Struck Capital F#{sub q})},
author = {Roche, Ph., E-mail: philippe.roche@univ-montp2.fr},
abstractNote = {We recall the relation between zeta function representation of groups and two-dimensional topological Yang-Mills theory through Mednikh formula. We prove various generalisations of Mednikh formulas and define generalization of zeta function representations of groups. We compute some of these functions in the case of the finite group GL(2, #Mathematical Double-Struck Capital F#{sub q}) and PGL(2, #Mathematical Double-Struck Capital F#{sub q}). We recall the table characters of these groups for any q, compute the Frobenius-Schur indicator of their irreducible representations, and give the explicit structure of their fusion rings.},
doi = {10.1063/1.4943294},
url = {https://www.osti.gov/biblio/22597042}, journal = {Journal of Mathematical Physics},
issn = {0022-2488},
number = 3,
volume = 57,
place = {United States},
year = {Tue Mar 15 00:00:00 EDT 2016},
month = {Tue Mar 15 00:00:00 EDT 2016}
}