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symmetricGroupTable -- character table of the symmetric group

Description

Returns the character table of the symmetric group $S_n$ over the field F. The irreducible characters are indexed by the partitions of $n$ written using a compact notation where an exponent indicates how many times a part is repeated. The computation uses the recursive Murnaghan-Nakayama formula.

i1 : symmetricGroupTable(4,QQ)

o1 = Character table over QQ
      
             |   6   8   3   6  1
     --------+-------------------
        (4)  |   1   1   1   1  1
      (3,1)  |  -1   0  -1   1  3
         2   |                  
       (2 )  |   0  -1   2   0  2
         2   |                  
     (2,1 )  |   1   0  -1  -1  3
         4   |                  
       (1 )  |  -1   1   1  -1  1

o1 : CharacterTable

If R is a polynomial ring, then symmetricGroupTable R calls symmetricGroupTable(numgens R,coefficientRing R). This is kept for compatibility with versions 2.1 and earlier of the package to create the character table of the symmetric group acting on the variables of R over the coefficient field of R.

See also

Ways to use symmetricGroupTable:

  • symmetricGroupTable(PolynomialRing)
  • symmetricGroupTable(ZZ,Ring)

For the programmer

The object symmetricGroupTable is a method function.

The source of this document is in /build/reproducible-path/macaulay2-1.26.05+ds/M2/Macaulay2/packages/BettiCharacters.m2:3859:0.