Quarks, diamonds, and representations of sl3
نویسنده
چکیده
A new model for the irreducible representations of sl3 is presented which is constructed over the integers. This model utilizes the combinatorial geometry of certain polytopes in three dimensional space which we call diamonds. These are not Gelfand-Tsetlin polytopes, but share some of their properties. Matrix coefficients are directly computable in terms of maximal ladders of edges of given directions and type in the diamonds. We show that the generic diamond is the vector sum of dilates of the fundamental diamonds associated to quark and anti-quark triples, and is simultaneously both a classical and quantum object.
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