Opened 2 years ago
Last modified 3 months ago
#30276 new enhancement
Phased permutation groups
Reported by: | Matthias Köppe | Owned by: | |
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Priority: | major | Milestone: | sage-9.8 |
Component: | combinatorics | Keywords: | |
Cc: | Travis Scrimshaw, Eric Gourgoulhon, Michael Jung, Léo Brunswic, Markus Wageringel, Dima Pasechnik, 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 (16)
comment:1 Changed 2 years ago by
Description: | modified (diff) |
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comment:2 Changed 2 years ago by
Description: | modified (diff) |
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comment:3 Changed 2 years ago by
Cc: | Léo Brunswic Markus Wageringel added |
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comment:4 Changed 2 years ago by
Cc: | Dima Pasechnik gh-Ivo-Maffei added |
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comment:5 Changed 2 years ago by
comment:7 Changed 2 years 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:9 Changed 2 years ago by
Would these be a generalization of ColoredPermutations
, where each element of {1, ..., n}
can have its own distinct cycle length?
comment:11 Changed 2 years ago by
Milestone: | sage-9.2 → sage-9.3 |
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comment:12 Changed 22 months ago by
Milestone: | sage-9.3 → sage-9.4 |
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Setting new milestone based on a cursory review of ticket status, priority, and last modification date.
comment:13 Changed 17 months ago by
Milestone: | sage-9.4 → sage-9.5 |
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comment:14 Changed 12 months ago by
Milestone: | sage-9.5 → sage-9.6 |
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comment:15 Changed 9 months ago by
Milestone: | sage-9.6 → sage-9.7 |
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comment:16 Changed 3 months ago by
Milestone: | sage-9.7 → sage-9.8 |
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this seems to generalise to cyclic groups only, no?