  
  [1X1 [33X[0;0YIntroduction[133X[101X
  
  [33X[0;0YThe  purpose  of  this  [5XGAP[105X  package  is  to  make a collection of [22Xp[122X-modular
  character  tables (Brauer tables) of spin-symmetric groups (and some related
  groups)  available  in  [5XGAP[105X, thereby extending Thomas Breuer's [5XGAP[105X Character
  Table  Library  [1]. The [5XSpinSym[105X package is based on [2] which serves as the
  general  reference  here.  If you are interested in computing with [5XSpinSym[105X I
  would  like  to  refer you to [2] for further references and a more thorough
  description  of  some  of  the topics below. And, of course, I would like to
  hear  from  you  about more or less successful attempts in using the present
  functionalities.[133X
  
  [33X[0;0YThe term `spin-symmetric' refers to the groups[133X
  
  
  [24X[33X[0;6Y2.Sym(n)= < z,t_1,...,t_n-1 : z^2=1, t_i^2=(t_it_i+1)^3=z, (t_jt_k)^2=z >[133X[124X
  
  [33X[0;0Yand[133X
  
  
  [24X[33X[0;6Y(2^+).Sym(n)= < z,t_1,...,t_n-1 : z^2=1, t_i^2=(t_it_i+1)^3=1, (t_jt_k)^2=z, zt_i=t_iz >[133X[124X
  
  [33X[0;0Ywhere  the  relations  are  imposed  for  all admissable [22Xi,j,k[122X with [22X|j-k|>1[122X.
  Provided  [22Xn≥ 4[122X, these groups are double covers of the symmetric group [22XSym(n)[122X
  on  [22Xn[122X  letters. Although [22X2.Sym(n)[122X and [22X(2^+).Sym(n)[122X are non-isomorphic groups
  for  [22Xn≠  6[122X,  they  are  isoclinic  and  their  representation theory is very
  similar. By [13Xchoice[113X, we restrict the attention to [22X2.Sym(n)[122X . (However, if you
  are  interested  in  character  tables  of  [22X(2^+).Sym(n)[122X then have a look at
  [10XCharacterTableIsoclinic()[110X in the [5XGAP[105X Reference Manual.)[133X
  
  [33X[0;0YThe  natural  epimorphism [22Xπ: 2.Sym(n) -> Sym(n), t_i↦ (i,i+1)[122X , whose kernel
  is  generated  by  the  central involution [22Xz[122X, gives rise to the double cover
  [22X2.Alt(n)=Alt(n)^{π^-1}[122X  of  the  alternating group [22XAlt(n)[122X as the preimage of
  [22XAlt(n)[122X under [22Xπ[122X. Irreducible faithful representations of [22X2.Sym(n)[122X or [22X2.Alt(n)[122X
  are called spin representations and a similar `spin' terminology is used for
  all  related  faithful  objects,  to  set  them  apart from the non-faithful
  objects that belong esssentially to [22XSym(n)[122X or [22XAlt(n)[122X, respectively.[133X
  
  
  [1X1.1 [33X[0;0YThe data part[133X[101X
  
  [33X[0;0YThe  package  contains complete Brauer tables of [22X2.Sym(n)[122X and [22X2.Alt(n)[122X up to
  degree  [22Xn=18[122X  in  characteristic [22Xp=3,5,7[122X. Thus it includes the corresponding
  Brauer  tables  of  [22XSym(n)[122X and [22XAlt(n)[122X. Moreover, Brauer tables of [22XSym(n)[122X and
  [22XAlt(n)[122X up to degree [22Xn=19[122X in characteristic [22Xp=2[122X are part of the package too.[133X
  
  [33X[0;0YEvery Brauer table comes with lists of character parameters (row labels) and
  class  parameters  (column labels), see [14X2.2[114X and [14X2.3[114X. I would like to mention
  that only some of the data is `new', large portions date back to the work of
  James,  Morris,  Yaseen,  and the Modular Atlas Project. Detailed references
  are  to  be  found  in  [2].  The  [22X2[122X-modular tables of [22XSym(n)[122X and [22XAlt(n)[122X for
  [22Xn=18,19[122X were computed jointly by Jürgen Müller and the author.[133X
  
  [33X[0;0YPlease  note that some of our Brauer tables differ to some extent from those
  contained  in  the [5XGAP[105X Character Table Library [1] (for example, in terms of
  the  ordering  of  conjugacy  classes  and  characters  or in terms of their
  parameters).  Therefore  it  seemed  appropriate  to collect these tables in
  their own package - so here we are.[133X
  
  [33X[0;0YI'm  grateful  to  Thomas  Breuer  for  supporting  the idea of writing this
  package  and  for  converting  my  tables into the right [5XGAP[105X Character Table
  Library format.[133X
  
  
  [1X1.2 [33X[0;0YThe functions part[133X[101X
  
  [33X[0;0YBesides  Brauer  tables,  the  package provides some related functionalities
  such  as functions that determine class fusions of subgroup character tables
  and  functions  that  compute  character  tables  of some Young subgroups of
  [22X2.Sym(n)[122X .[133X
  
  
  [1X1.3 [33X[0;0YInstallation and loading[133X[101X
  
  [33X[0;0YTo  install this package, download the archive file [9Xspinsym-1.5.2.tar.gz[109X and
  unpack it inside the [9Xpkg[109X subdirectory of your [5XGAP[105X installation. It creates a
  subdirectory  called  [9Xspinsym[109X.  Then  load the package using the [9XLoadPackage[109X
  command.[133X
  
  [4X[32X  Example  [32X[104X
    [4X[28X[128X[104X
    [4X[25Xgap>[125X [27XLoadPackage("spinsym");[127X[104X
    [4X[28X[128X[104X
  [4X[32X[104X
  
  [33X[0;0YThe  [5XSpinSym[105X package banner should appear on the screen. You may want to run
  a quick test of the installation:[133X
  
  [4X[32X  Example  [32X[104X
    [4X[28X[128X[104X
    [4X[25Xgap>[125X [27Xdir:= DirectoriesPackageLibrary( "spinsym", "tst" )[1];;[127X[104X
    [4X[25Xgap>[125X [27Xtst:= Filename( dir, "testall.tst" );;[127X[104X
    [4X[25Xgap>[125X [27XTest( tst );[127X[104X
    [4X[28Xtrue[128X[104X
    [4X[28X[128X[104X
  [4X[32X[104X
  
