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Re: Implementation Question  SL(2,C)

To: rminer@geom.umn.edu, w3cmatherb@w3.org

Subject: Re: Implementation Question  SL(2,C)

From: ion@math.ams.org (Patrick D. F. Ion)

Date: Wed, 03 Jul 1996 18:36:21 0400

From ion@math.ams.org Wed Jul 3 18: 32:37 1996

MessageId: <v02130508ae00985410c6@[130.44.25.36]>

XSender: ion@mr4.mr.ams.org
The case of SL(2,C) brings up a couple of questions aside from accents. I
note that Robert's display list shows a bold C, presumably for the complex
numbers, as, for instance, MR style prescribes. However, many choose a
blackboard bold or doublestruck font, and so then there's an argument for
hoping that people might consider a math entity ℂ which the
reader could display in the locally favored way.
In contrast to MR, Robert did not choose to put the _abbreviation_, SL,
naming the classical Special Linear group in roman, as opposed to a
presumed italic within a mathematical expression. Again one could argue
here for a math entity &SL;. This notation is probably understood most
commonly as a certain 2 x 2 matrix group. The placement of the 2 for the
dimension is often as a subscript, i.e., SL_2(\bbf C) is common.
You can argue that the (.,.) notation just gives a pair as an argument to a
functor SL, so the comma is part of the math notation for a pair, or you
can make other arguments for the treatment of the comma.
When it comes to accenting expressions like SL(2,C) opinions differ here too.
The quantum group ${\rm SL}_q(2,{\bf C})$ has been seen, and the space of
unitary representations $SL(2,C)\hat{}$, where the hat is postfixed rather
than spanning; and then there are constructions like $\widetilde{SL(2,C)}$
where it seems that there is a feeling that the ~ cannot operate as a
postfix but has to be a sort of lid over the whole expression (leading to
abominations like
$\widetilde{{\rm U}(1) \times {\rm SU}(2) \times {\rm SU}(2)}$).
And so on:
you have to allow specification of embellishment placement, and I think it
is desirable to allow what Nico nicely distinguishes as over and
underline
elements as well as accents (stackable, for Vietnamese at least). Of course,
in Unicode there are fonts full of fully accented characters, I believe,
aside from their presence in the ISO Latins etc.
Patrick
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