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I think “(in representation theory)” could be improved to instead use the mathematically defined names rather than subfield description. First of all the usable notions are root system, coroot, weight lattice, dominant weight and weight of a representation (with redirect weight of a module), all different from ambiguous root and weight and better than weak root (in representation theory). These are well established mathematical notions, while somewhat arbitrary and descriptive “weight in representation theory” is ad hoc title for a school lecture. Second, root system is not necessarily used in representation theory; they are used in structure theory of Lie groups, classification of symmetric spaces, in study of reflections and symmetries in Euclidean spaces, classification of Lagrangean singularities, study of Coxeter groups and so on, often without any representation ever mentioned. So I would prefer to cover the subject within the mathematical network of well established notions like root system, root datum, coroot, simple root etc. rather than the arbitrary nonmathematical but descriptive partitioning.
This is specially important because $n$Lab is supposed to cover the big picture of mathematics and not the hot topics or viewpoints from a particular field. Here the root systems for example, have their meaning and applications much beyond solely representation theory, and especially beyond just the representation theory of finite dimensional Lie algebras (And in no case I would consider somebody like Peter Woit to be much relevant for the terminology in such a central field in mathematics.)
What do you think ? I would like to proceed with refining and renaming the circle of entries.
I was just following the practice on Wikipedia. But all this is stubs anyway, so all this is yours to work on!
Well, yes, I was suspecting this, wikipedia wants to have a word for every notion separately. So if we want to have structly ’root’ in both meanings under root we need to follow the wikipedia style. But the root in this second meaning may be covered under root system with possibly a wikipedia style redirect. We have a bit more freedom :) I’ll go on soon to refine our circle…
But in entries on root systems authors are likely to – no: certainly will – refer to a root.
It’s good to have the entry system assume as little as possible on the reader…
No problem with that. I said clearly that a redirect is OK. Just it is not a canonical mathematical title.
Even Wikipedia is supposed to use descriptive terms like Zoran is advocating when these are available. Too much parentheses there is a sign of laziness. (Also, Wikipedia would not use the preposition ‘in’).
“lasiness”? Has your preference for -ise over -ize gotten the better of you, Toby? :-)
Sorry, I confused ‘lazy’ with ‘cosy’.
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