# Re: Implementation Question -- SL(2,C)

• To: rminer@geom.umn.edu, w3c-math-erb@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
• Message-Id: <v02130508ae00985410c6@[130.44.25.36]>
• X-Sender: 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 &complexes; 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
under-line
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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