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Order of Irreducible Representation Characters wrong in Sage?

I am using Sage to calculate Irreducible Representations (IRR) of symmetry groups of graphs. Most of the time the order of the IRR characters match the order of the conjugacy class representatives. For example the trivial representation characters are the first row of the character table (1,1,1,1,...,1) and the first conjugacy class is ( ), the identity representation. But in the example below for a star graph (one central vertex, the 4 other vertices on spokes from the center) the trivial representation characters are the last row in the character table and the conjugacy class representatives have the identity as the first element.

Example (star graph).

ct=G.character_table() print ct

[ 1 -1 1 1 -1] [ 3 -1 -1 0 1] [ 2 0 2 -1 0] [ 3 1 -1 0 -1] [ 1 1 1 1 1] <--- trivial rep. is last

cc=G.conjugacy_classes_representatives() print cc

[(), (1,2), (1,2)(3,4), (1,2,3), (1,2,3,4)] ^ trivial class is first

Is this a bug or known issue for Sage? How can I get around it so I know the orders of the characters and representatives match up properly?

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updated 2012-09-06 04:48:42 -0500

kcrisman gravatar image

Order of Irreducible Representation Characters wrong in Sage?

I am using Sage to calculate Irreducible Representations (IRR) of symmetry groups of graphs. Most of the time the order of the IRR characters match the order of the conjugacy class representatives. For example the trivial representation characters are the first row of the character table (1,1,1,1,...,1) and the first conjugacy class is ( ), the identity representation. But in the example below for a star graph (one central vertex, the 4 other vertices on spokes from the center) the trivial representation characters are the last row in the character table and the conjugacy class representatives have the identity as the first element.

Example (star graph).

ct=G.character_table()
print ct

ct [ 1 -1 1 1 -1] [ 3 -1 -1 0 1] [ 2 0 2 -1 0] [ 3 1 -1 0 -1] [ 1 1 1 1 1] <--- trivial rep. is last

last cc=G.conjugacy_classes_representatives() print cc

cc [(), (1,2), (1,2)(3,4), (1,2,3), (1,2,3,4)] ^ trivial class is first

first

Is this a bug or known issue for Sage? How can I get around it so I know the orders of the characters and representatives match up properly?