MapHW
Generates the Gelfand-Zetlin Tableau, applies the operators from the tableu to the highest weight vector, and solves the Borel condition.

Calling Sequence

MapHW ( [Topline, Tensors], [Verbosity_Level] );

Parameters

Irrep	List in the form [t1,t2,t3,...]
Tensors	List of lists in the form [[a1,a2,...], [b1,b2,...], [...], ...]
Verbosity_Level	Either identically Verbose, or Terse

Description

• Irrep is the irreducible representation that one is interested in the multiplicity of. It becomes the topline of each of the Gelfand-Zetlin Tableau and must be a list of integers that are monotonically decreasing.
   
• Tensors becomes the bottom line of each Tableau after zeros are removed and the lists are concatonated. Tensors should be a list of the signatures of the representations in the tensor product, where each signature is also given as a list of monotonically decreasing integers. In addition, the weight (sum) of all these integers must equal the sum of all integers in Irrep, and the number of non-zero integers in Tensors must equal the number of entries in Irrep.
   
• Verbosity Levels are defined as follows:

  Terse

  At various points in the procedure, the progress is displayed along with the time stamp of when the message was displayed. For large examples, this allows the user to ensure that the computer is still working and to compare the lengths of time each part of the prodecure takes.

  Verbose

  The feedback normaly displayed in Terse mode during the procedure is generally suppressed, except in larger examples. If the procedure sences that to much time has elapsed since the last feedback, it will still display some progress. In any case, after the results are determined, various data is displyed, including the highest weight vector, some of the tableau, and some of the resultant polynomials.
   

• If a Verbosity level is not specified, the procedure will default to Terse mode.
   
• If Irrep and Tensors are not explicitly passed, the procedure will run in "shorthand" mode. In this case, the global variables by the same names (Irrep and Tensors) will be used, causing an error if they are not already defined. In shorthand mode, the procedure will also only returned the length of time the calculation took.
   
• When Irrep and Tensors are explicitly passed, the procedure returns four values, M, Δ, B, and (πL). These are defined such that Φ = M · Δ = B · (πL) f_max. However, the other procedures are designed to automatically use the recent results of MapHW, and so there is little functional use of the user accessing these values. Furthermore, Δ and (πL) are returned as encoded by the procedure. See Additional Documentation for details of the encoding process.
   

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