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mathematical analysis > function > symmetric function > Jucys-Murphy element

algebra > representation theory > group representation > Jucys-Murphy element

... > combinatorics > permutation > symmetric group > permutation group > Jucys-Murphy element

... > combinatorics > permutation > symmetric group > permutation group > Jucys-Murphy element

algebra > group theory > finite group > permutation group > Jucys-Murphy element

Preferred term

Jucys-Murphy element

Definition(s)

In mathematics, the Jucys–Murphy elements in the group algebra ${\\displaystyle \\mathbb {C} [S_{n}]}$ of the symmetric group, named after Algimantas Adolfas Jucys and G. E. Murphy, are defined as a sum of transpositions by the formula:

${\\displaystyle X_{1}=0,~~~X_{k}=(1\\;k)+(2\\;k)+\\cdots +(k-1\\;k),~~~k=2,\\dots ,n.}$

They play an important role in the representation theory of the symmetric group.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Jucys%E2%80%93Murphy_element)

Broader concept(s)

In other languages

élément de Jucys-Murphy

French

URI

http://data.loterre.fr/ark:/67375/PSR-M9WLXDDG-X

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