• Question: what is representation theory and what is it used for?

    Asked by to Ian, Naomi on 27 Jun 2014. This question was also asked by .
    • Photo: Ian Stephenson

      Ian Stephenson answered on 27 Jun 2014:

      I’ve not come across it before, but it looks like its basically a way of doing group theory by substituting vector/matrix algebra for more abstract notations – but you know that right…

      I can’t answer specifically, but heres some background that might help:

      Group theory is a really cool/abstract part of maths that deals with the questions “what is maths?”. Rather than just having + to mean add, it asks the question what COULD + mean? It’s something that combines two other things (numbers) and gives a results that is another thing (again usually, but not always a number). We make no assumptions about what + might actually mean, but rather start with one or two things that we decide are true (for example we might decide that 1+1 is 2) called axioms and see what happens.

      It turns out that some things we take for granted aren’t always true – for example, you know that AxB=BxA? Well not if A wasn’t just a simple number – what if A was walk forwards 2m, and B was turn right 90 degrees, then doing them in one order is different from doing them in the other order. Matices/Vectors can be used to represent things like move and turn (this is the fundamentals of computer graphics), and in this case the order we multiply in is important.

      So not all “versions” of maths work the same. Group theory looks at these different versions of maths.

      From a quick scan of the Wikipedia page (OK the first paragraph!), it sounds like Representation theory is saying that there kinds of maths, where the maths itself can be described as matrices, so you can they’re an easier way to do maths about maths.

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