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> restart:with(group):with(SymGroupAlgebra); _known_types Algebraic listbasmon cycbasmon cycmon cycpolynom tabloid tabloidmon, , , , , , ,[=
 

Summary: > restart:with(group):with(SymGroupAlgebra);
_known_types Algebraic listbasmon cycbasmon cycmon cycpolynom tabloid tabloidmon, , , , , , ,[=
polytabloid tableau standardtableau generalizedtableau generalizedtableaumon, , , , ,
polygeneralizedtableau semistandardtableau partition, , ]
_known_conversions convert/t_to_tabloid convert/t_to_generalizedtableau, ,[=
convert/t_to_matrix convert/m_to_tableau convert/cycbasmon_to_listbasmon, , ,
convert/listbasmon_to_cycbasmon]
ActionOnGeneralizedTableau ActionOnTableau ActionOnTabloid ColumnStabilizer, , , ,[
GroupProduct Hminus Hplus ModuleLoad ModuleUnload PermGroup RowStabilizer, , , , , , ,
SGAversion YoungSubgroup associated_polytabloid conjugation content_of disjcycform fdim, , , , , , ,
is_partition_of kappa_action make_standard_fill makepartitions pbasis pcollect pinv pmul, , , , , , , , ,
rowdescent sgn shape_of size split tableautranspose transversal, , , , , , ]
>
This is a preliminary attempt to write a small package for computation with a group algebra of the
symmetric group S[n]. This package relies on Maple's "group" package which allows for computation
in the symmetric group S[n] but not in the group algebra of S[n]. In particular, this package uses the
following commands from the "group" package:
- mulperms - for multiplying permutations written in disjoint cycle notation, e.g., [[1,2],[3,4,5]], []
(identity element); it is used in procedure 'pmul',
- invperm - for finding inverse of a permutation written in disjoint cycle notation; it is used in

  

Source: Ablamowicz, Rafal - Department of Mathematics, Tennessee Technological University

 

Collections: Mathematics