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Linear representation theory of monster group

Revision as of 21:32, 31 March 2012 by Vipul (talk | contribs)

Summary

Item Value
degrees of irreducible representations (too long to list -- see #GAP implementation)
number: 194, sum of squares of degrees of irreducible representations equals order of group: 808017424794512875886459904961710757005754368000000000, maximum degree of irreducible representation: 258823477531055064045234375, quasirandom degree: 196883

GAP implementation

Degrees of irreducible representations

The monster group itself is not stored in GAP, but some information on its irreducible representations is, and we use the symbol "M" to access this information. The degrees of irreducible representations can be computed using the CharacterDegrees and CharacterTable functions.

gap> CharacterDegrees(CharacterTable("M"));
[ [ 1, 1 ], [ 196883, 1 ], [ 21296876, 1 ], [ 842609326, 1 ], [ 18538750076, 1 ], [ 19360062527, 1 ], [ 293553734298, 1 ], [ 3879214937598, 1 ],
  [ 36173193327999, 1 ], [ 125510727015275, 1 ], [ 190292345709543, 1 ], [ 222879856734249, 1 ], [ 1044868466775133, 1 ], [ 1109944460516150, 1 ],
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