  
  [1X1 Introduction[0X
  
  This manual describes the [5XRepsn[0m package for computing matrix representations
  in characteristic zero of finite groups. Most of the functions in [5XRepsn[0m have
  been  written  according  to  the  algorithm  described in the author's Ph.D
  thesis [Dab-03] and [DD-08] (see [Dab-05]).
  
  For  constructing  representations  of simple groups and their covers we use
  the  algorithm described in [Dix-93]. To use this algorithm for constructing
  a  representation  of a group G affording an irreducible character chi of G,
  we  need to have a subgroup H of G such that the restriction of chi to H has
  a  linear  constituent  with  multiplicity  one.  In this case we say H is a
  [13Xcharacter  subgroup[0m  relative to chi (or a chi-subgroup). A chi-subgroup for
  each  irreducible character chi of degree less than 100 of simple groups and
  their covers are listed in [Dab-06] and [Dab-07].
  
  All  [5XRepsn[0m  functions are written entirely in the [5XGAP[0m language. It is proved
  in  [Dab-05]  and [DD-08] that the algorithm is correct for any group with a
  character  of  degree less than 100. Indeed, if the group is solvable, there
  is  no restriction on the character degree. In practice the program is quite
  fast  when the degree is small, but can be very slow when it is necessary to
  call one of the subprograms which extend irreducible representations. In the
  latter  case  the  number  of  element  wise operations required to extend a
  representation of degree d is proportional to d^6.
  
  [5XRepsn[0m  is implemented in the [5XGAP[0m language, and runs on any system supporting
  [5XGAP[0m4.  The  [5XRepsn[0m  package  is  loaded into the current [5XGAP[0m session with the
  command
  
   gap> LoadPackage( "repsn" ); 
  
  (see  section  [13XLoading a GAP Package[0m in the [5XGAP[0m Reference Manual). One could
  install  the  [5XRepsn[0m  package  on  [5XGAP[0m4.3. In this case it is loaded with the
  command
  
   gap> RequirePackage( "repsn" ); 
  
  [5XRepsn[0m has been developed by
  
  Vahid Dabbaghian
  Department of Mathematics
  Simon Fraser University
  Burnaby, British Columbia,
  V5A 1S6 Canada.
  e-mail: vdabbagh@sfu.ca
  
  Please  send  bug  reports,  suggestions  and  other comments to this e-mail
  address.
  
