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symmetricGroupTable -- character table of the symmetric group

Synopsis

Description

Returns the character table of the symmetric group $S_n$, where $n$ is the number of variables of the polynomial ring in the input. 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 : R=QQ[x_1..x_4]

o1 = R

o1 : PolynomialRing
 
i2 : symmetricGroupTable(R)

o2 = Character table over R
      
             |   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

o2 : CharacterTable

See also

Ways to use symmetricGroupTable :

For the programmer

The object symmetricGroupTable is a method function.