Opened 4 months ago
Last modified 3 months ago
#30276 new enhancement
Phased permutation groups
Reported by: | mkoeppe | Owned by: | |
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Priority: | major | Milestone: | sage-9.3 |
Component: | combinatorics | Keywords: | |
Cc: | tscrim, egourgoulhon, gh-mjungmath, gh-LBrunswic, gh-mwageringel, dimpase, gh-Ivo-Maffei | Merged in: | |
Authors: | Reviewers: | ||
Report Upstream: | N/A | Work issues: | |
Branch: | Commit: | ||
Dependencies: | Stopgaps: |
Description (last modified by )
Mathematica uses "phased permutations" to express tensor symmetries.
A cycle of length k is labeled with a kth root of unity.
http://reference.wolframcloud.com/language/tutorial/TensorSymmetries.html
This generalizes the symmetries that sage.tensor
can currently express, which are products of full symmetric groups (where the transpositions in the antisymmetries are labeled with -1).
We represent it as a matrix group in GL_n,
and also provide a method that computes its representation as a subgroup of GL(T^{k,l)M)
.
Related reference: https://arxiv.org/pdf/2007.08056.pdf
Change History (11)
comment:1 Changed 4 months ago by
- Description modified (diff)
comment:2 Changed 4 months ago by
- Description modified (diff)
comment:3 Changed 4 months ago by
- Cc gh-LBrunswic gh-mwageringel added
comment:4 Changed 4 months ago by
- Cc dimpase gh-Ivo-Maffei added
comment:5 Changed 4 months ago by
comment:6 Changed 4 months ago by
each generator is a cycle...
comment:7 Changed 4 months ago by
each generator is a product of cycles, in full generality. Then, I think these things are called monomial groups, "phased" comes from physics people not taking algebra classes :-)
comment:8 Changed 4 months ago by
Yes, it's a Wolfram-ism, I think
comment:9 Changed 4 months ago by
Would these be a generalization of ColoredPermutations
, where each element of {1, ..., n}
can have its own distinct cycle length?
comment:10 Changed 4 months ago by
yes, but with some kind of compatibility relation, I guess.
comment:11 Changed 3 months ago by
- Milestone changed from sage-9.2 to sage-9.3
this seems to generalise to cyclic groups only, no?