ICMT Seminar: "Hermitian Young symmetrizers and Jucys-Murphy elements."
(sign-up)Prof. Mike Stone, University of Illinois, Urbana Champaign
Institute for Condensed Matter Physics
Young tableaux and Young symmetrisers have many applications in physics -- ranging from the Bethe ansatz through bosonization and integrable systems to computing group-combinatorial factors in Feynman diagrams. The properties of these objects were thoroughly explored by Young, Frobenius, Schur and Littlewood in the first half of the twentieth century. It is therefore perhaps surpring that a number of papers with new results and algorithms have appeared recently on the archive (arXiv:1610.10088, arXiv:1610.08802, arXiv:1307.6147). In this talk I will describe the history (some of it personal) and the mathematics (suprisingly simple) that lies behind the recent work. In particular I will describe the construction of hermitian Young projectors from the Jucys-Murphy elements of the algebra of the symmetric group.
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