Opened 4 months ago

Last modified 3 months ago

#30276 new enhancement

Phased permutation groups

Reported by: mkoeppe Owned by:
Priority: major Milestone: sage-9.3
Component: combinatorics Keywords:
Cc: tscrim, egourgoulhon, gh-mjungmath, gh-LBrunswic, gh-mwageringel, dimpase, gh-Ivo-Maffei Merged in:
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Description (last modified by mkoeppe)

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 mkoeppe

  • Description modified (diff)

comment:2 Changed 4 months ago by mkoeppe

  • Description modified (diff)

comment:3 Changed 4 months ago by mkoeppe

  • Cc gh-LBrunswic gh-mwageringel added

comment:4 Changed 4 months ago by mkoeppe

  • Cc dimpase gh-Ivo-Maffei added

comment:5 Changed 4 months ago by dimpase

this seems to generalise to cyclic groups only, no?

comment:6 Changed 4 months ago by mkoeppe

each generator is a cycle...

comment:7 Changed 4 months ago by dimpase

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 mkoeppe

Yes, it's a Wolfram-ism, I think

comment:9 Changed 4 months ago by tscrim

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 mkoeppe

yes, but with some kind of compatibility relation, I guess.

comment:11 Changed 3 months ago by mkoeppe

  • Milestone changed from sage-9.2 to sage-9.3
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