HELP FOR: A package to handle characters of the linear group.

CALLING SEQUENCE:

CLG[<function>](args)

<function>(args)

SYNOPSIS:

• This package provides functions to manipulate characters of the linear group GL(n). It essentially amounts to consider symmetric functions in a fixed number of variables.

• One chooses the order using the function CLG_n (default degree is 5).

• Whenever there is a conflict between a function name in CLG and another name used in the same session, use the long form CLG[<function>].

• The available functions are:

  CLG_n	Gauss	GlDimRep	Toe_n
  Toh_n	Tom_n	Top_n	Tos_n
  Tox_n	x2m_n

• For help with a particular function do either ?CLG[<function>] or ?CLG,<function> where <function> is one from the above list.

EXAMPLES:

> with(CLG):
> CLG_n(5);
 
                                       5
 
> Tos_n(s[4,3,2,1,1]^2, collect);
 
     3 s[6, 6, 5, 3, 2] + 2 s[6, 6, 4, 4, 2] + 3 s[6, 6, 4, 3, 3]
 
   + 3 s[6, 5, 5, 4, 2] + 3 s[6, 5, 5, 3, 3] + 4 s[6, 5, 4, 4, 3]
 
   + 4 s[7, 6, 4, 3, 2] + 3 s[7, 5, 5, 3, 2] + 2 s[7, 6, 3, 3, 3]
 
   + 3 s[7, 5, 4, 4, 2] + 4 s[7, 5, 4, 3, 3] + s[8, 6, 3, 3, 2]
 
   + s[8, 6, 4, 2, 2] + s[5, 5, 5, 5, 2] + 2 s[5, 5, 5, 4, 3]
 
   + s[5, 5, 4, 4, 4] + s[6, 4, 4, 4, 4] + 2 s[7, 4, 4, 4, 3]
 
   + s[7, 7, 4, 2, 2] + s[7, 7, 3, 3, 2] + 2 s[7, 6, 5, 2, 2]
 
   + s[8, 5, 5, 2, 2] + 2 s[8, 5, 4, 3, 2] + s[8, 5, 3, 3, 3]
 
   + s[8, 4, 4, 4, 2] + s[8, 4, 4, 3, 3] + s[6, 6, 6, 2, 2]