Are subtypes of Cartan types implemented correctly?

asked 2018-11-06 16:38:28 +0100

pbelmans
25 ●1 ●4

Consider the following code

CartanType("B3").subtype([2, 3]).index_set()
CartanType("B3").subtype([1, 3]).index_set()

It gives

(2, 3)
(1, 2)

in Sage 8.4. Is it wrong to expect the index set of a subtype to be the subset used in defining the subtype? From my point of view this inconsistency leads to all kinds of unexpected behaviour in the relabellings for subtypes, but maybe it is intentional?

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answered 2018-11-08 21:46:13 +0100

FrédéricC

5206 ●3 ●43 ●114

It seems that currently the index set for reducible types can only be consecutive integers starting from 1.

sage: ct = CartanType("B3").subtype([1, 3])
sage: ct.index_set??

This is displayed also in the following example

sage: CartanType("A5").index_set()
(1, 2, 3, 4, 5)
sage: CartanType("A5").subtype([3,4]).index_set()
(3, 4)
sage: CartanType("A5").subtype([1,4]).index_set()
(1, 2)

So there is certainly room for improvement here.

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Thanks! We'll just work around it for now, maybe I'll have a go at improving Sage in the future.

pbelmans ( 2018-11-12 10:35:10 +0100 )edit

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Asked: 2018-11-06 16:38:28 +0100

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Last updated: Nov 08 '18

Are subtypes of Cartan types implemented correctly? edit