Young Tableau
For the symmetric groups, a graphical method exists to determine their finite representations that associates with each representation a Young tableau (also known as a Young diagram). The direct product of two representations may easily be decomposed into a direct sum of irreducible representation by a set of rules for the "direct product" of two Young diagrams. Each diagram also contains information about the dimension of the representation to which it corresponds. Young tableaux provide a far cleaner way of working with representations than the algebraic methods that underlie their use.
Read more about this topic: Representation Theory Of Finite Groups
Famous quotes containing the word young:
“Pleasure is the rock which most young people split upon; they launch out with crowded sails in quest of it, but without a compass to direct their course, or reason sufficient to steer the vessel; for want of which, pain and shame, instead of pleasure, are the returns of their voyage.”
—Philip Dormer Stanhope, 4th Earl Chesterfield (1694–1773)