48.52 MOCTable

MOCTable( gaptbl )
MOCTable( gaptbl, basicset )

return the MOC format table record of the GAP table gaptbl, and stores it in the component MOCtbl of gaptbl.

The first form can be used for ordinary (G.0) tables only, for modular (G.p) tables one has to specify a basic set basicset of ordinary irreducibles which must be the list of positions of these characters in the irreducibles component of the corresponding ordinary table (which is stored in gaptbl.ordinary).

The result contains the information of gaptbl in a format similar to the MOC 3 format, the table itself can e.g. easily be printed out or be used to print out characters using PrintToMOC.

The components of the result are

identifier :

the string MOCTable( name ) where name is the identifier component of gaptbl,

isMOCformat :

has value true,

GAPtbl :

the record gaptbl,

operations :

equal to MOCTableOps, containing just an appropriate Print function,

prime :

the characteristic of the field (label 30105 in MOC),

centralizers:

centralizer orders for cyclic subgroups (label 30130)

orders :

element orders for cyclic subgroups (label 30140)

fields :

at position i the number field generated by the character values of the i--th cyclic subgroup; the base component of each field is a Parker base, (the length of fields is equal to the value of label 30110 in MOC).

cycsubgps :

cycsubgps[i] = j means that class i of the GAP table belongs to the j--th cyclic subgroup of the GAP table,

repcycsub :

repcycsub[j] = i means that class i of the GAP table is the representative of the j--th cyclic subgroup of the GAP table. Note that the representatives of GAP table and MOC table need not agree!

galconjinfo :

a list [ r_1,c_1,r_2,c_2,ldots,r_n,c_n ] which means that the i--th class of the GAP table is the c_i--th conjugate of the representative of the r_i--th cyclic subgroup on the MOC table. (This is used to translate back to GAP format, stored under label 30160)

30170 :

(power maps) for each cyclic subgroup (except the trivial one) and each prime divisor of the representative order store four values, the number of the subgroup, the power, the number of the cyclic subgroup containing the image, and the power to which the representative must be raised to give the image class. (This is used only to construct the 30230 power map/embedding information.) In result.30170 only a list of lists (one for each cyclic subgroup) of all these values is stored, it will not be used by GAP.

tensinfo :

tensor product information, used to compute the coefficients of the Parker base for tensor products of characters (label 30210 in MOC). For a field with vector space base (v_1,v_2,ldots,v_n) the tensor product information of a cyclic subgroup in MOC (as computed by fct) is either 1 (for rational classes) or a sequence [ n x_1,1 y_1,1 z_1,1 x_1,2 y_1,2 z_1,2 ldots x_1,m_1 y_1,m_1 z_1,m_1 0 x_2,1 ldots z_2,m_2 0 ldots x_n,m_n y_n,m_n z_n,m_n 0 ] which means that the coefficient of v_k in the product [ ( sum_i=1^n a_i v_i ) ( sum_j=1^n b_j v_j ) ] is equal to [ sum_i=1^m_k x_k,i a_y_k,i b_z_k,i . ] On a MOC table in GAP the tensinfo component is a list of lists, each containing exactly the sequence

invmap :

inverse map to compute complex conjugate characters, label 30220 in MOC.

powerinfo :

field embeddings for p--th symmetrizations, p prime in [ 2 .. 19 ]; note that the necessary power maps must be stored on gaptbl to compute this component. (label 30230 in MOC)

30900 :

basic set of restricted ordinary irreducibles in the case of nonzero characteristic, all ordinary irreducibles else.

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