%0 Journal Article
%T Generalized Zeta function representation of groups and 2-dimensional Topological Yang-Mills theory: The example of GL(2, F_q) and PGL(2, F_q)
%+ Laboratoire Charles Coulomb (L2C)
%+ Institut Montpelliérain Alexander Grothendieck (IMAG)
%A Roche, Philippe
%< avec comité de lecture
%Z L2C:15-229
%@ 0022-2488
%J Journal of Mathematical Physics
%I American Institute of Physics (AIP)
%V 57
%N 3
%P Article number 031701
%8 2016-03-15
%D 2016
%Z 1512.03811
%R 10.1063/1.4943294
%Z Mathematics [math]/Representation Theory [math.RT]
%Z Physics [physics]/High Energy Physics - Theory [hep-th]
%Z Physics [physics]/Mathematical Physics [math-ph]
%Z Mathematics [math]/Mathematical Physics [math-ph]Journal articles
%X 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 functions representations of groups. We compute some of these functions in the case of the finite group $GL(2, {\mathbb F}_q)$ and $PGL(2,{\mathbb F}_q).$ 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
%G English
%L hal-01250756
%U https://hal.science/hal-01250756
%~ CNRS
%~ I3M_UMR5149
%~ L2C
%~ IMAG-MONTPELLIER
%~ TDS-MACS
%~ MIPS
%~ UNIV-MONTPELLIER
%~ UM-2015-2021