precond - Precondensation of Tensor Products"

Command Line

precond Options Info M N 

Options
Standard options, see Standard Command Line Options
Info
Name of the tensor condensation data file.
M
Name of first module (left factor).
N
Name of second module (right factor).

Input Files

M.cfinfo, N.cfinfo
Constituent information.
MCf.std.1, MCf.std.2, ..., NCf.std.1, NCf.std.2, ...
Standard generators of the condensation subgroup H for each constituent.

Output Files

Info.tki
Tensor condensation info file.
Info.q.1, Info.q.2, ...
Embeddings for each constituent.
Info.p.1, Info.p.2, ...
Projections for each constituent.

Description

This program performs two tasks:

Implementation Details

Step 1, matching of constituents, is implemented in the same way as in chop and cfcomp, i.e., by using the standard basis with respect to identifying words. Step 2 is based on two observations:

From (A) it is clear that calculating the embedding of (S⊗T)eH into S⊗T is equivalent to computing a basis of EndkH(V). The latter is easily accomplished using the peak word of V. As a consequence of the second observation, there is a natural one-to-one correspondence between H-invariant linear forms on Hom_k(V,V) and EndkH(V), which is used to calculate the projection from Homk(V,V) on EndkH(V).

More details on the algorithm used in Step 2 can be found in [Ri98].


MeatAxe 2.4 documentation, generated on Tue May 12 01:29:54 2009