In mathematics, the Jucys–Murphy elements in the group algebra C [ S n ] {\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: X 1 = 0 , X k = ( 1 k ) + ( 2 k ) + ⋯ + ( k − 1 k ) , k = 2 , … , n . {\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.
In mathematics, the Jucys–Murphy elements in the group algebra C [ S n ] {\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: X 1 = 0 , X k = ( 1 k ) + ( 2 k ) + ⋯ + ( k − 1 k ) , k = 2 , … , n . {\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.
Source: Wikipedia "Jucys–Murphy element" · CC BY-SA 4.0
Share this article: X · Bluesky