Opened 2 years ago

Last modified 3 months ago

#30276 new enhancement

Phased permutation groups

Reported by: Matthias Köppe Owned by:
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:
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Report Upstream: N/A Work issues:
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Description (last modified by Matthias Köppe)

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 Matthias Köppe

Description: modified (diff)

comment:2 Changed 2 years ago by Matthias Köppe

Description: modified (diff)

comment:3 Changed 2 years ago by Matthias Köppe

Cc: Léo Brunswic Markus Wageringel added

comment:4 Changed 2 years ago by Matthias Köppe

Cc: Dima Pasechnik gh-Ivo-Maffei added

comment:5 Changed 2 years ago by Dima Pasechnik

this seems to generalise to cyclic groups only, no?

comment:6 Changed 2 years ago by Matthias Köppe

each generator is a cycle...

comment:7 Changed 2 years ago by Dima Pasechnik

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 2 years ago by Matthias Köppe

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

comment:9 Changed 2 years ago by Travis Scrimshaw

Would these be a generalization of ColoredPermutations, where each element of {1, ..., n} can have its own distinct cycle length?

comment:10 Changed 2 years ago by Matthias Köppe

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

comment:11 Changed 2 years ago by Matthias Köppe

Milestone: sage-9.2sage-9.3

comment:12 Changed 22 months ago by Matthias Köppe

Milestone: sage-9.3sage-9.4

Setting new milestone based on a cursory review of ticket status, priority, and last modification date.

comment:13 Changed 17 months ago by Matthias Köppe

Milestone: sage-9.4sage-9.5

comment:14 Changed 12 months ago by Matthias Köppe

Milestone: sage-9.5sage-9.6

comment:15 Changed 9 months ago by Matthias Köppe

Milestone: sage-9.6sage-9.7

comment:16 Changed 3 months ago by Matthias Köppe

Milestone: sage-9.7sage-9.8
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