C. R. Math. Rep. Acad. Sci. Canada Vol. 39 (1) 2017, pp. 13-35
March 31, 2017
Nathan Grieve,Department of Mathematics and Statistics, University of New Brunswick, Fredericton, NB,Canada E3B 5A3; e-mail: n.grieve@unb.ca
Abstract/Résumé:
We study the infinite wedge representation and show how it is related to the universal central extension of \(g[t,t^{-1}]\), the loop algebra of a complex semi-simple Lie algebra \(g\). We also give an elementary proof of the boson-fermion correspondence. Our approach to proving this result is based on a combinatorial construction combined with an application of the Murnaghan-Nakayama rule.
Nous étudions l’algèbre extérieure en dimension infinie et montrons comment elle est reliée à l’extension centrale universelle de \(g[t,\!t^{-1}]\), l’algèbre de lacets sur une algèbre de Lie \(g\) semi-simple complexe. De plus, nous donnons une preuve élémentaire de la correspondance boson-fermion. Pour ce faire, nous utilisons une construction combinatoire, ainsi que la règle de Murnaghan-Nakayama.
AMS Subject Classification: Symmetric functions, Completely integrable systems; integrability tests; bi-Hamiltonian structures; hierarchies (KdV; KP; Toda; etc.) 05E05, 37K10
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