Significance
The traditional application of Young's lattice is to the description of the irreducible representations of symmetric groups Sn for all n, together with their branching properties, in characteristic zero. The equivalence classes of irreducible representations may be parametrized by partitions or Young diagrams, the restriction from Sn + 1 to Sn is multiplicity-free, and the representation of Sn with partition p is contained in the representation of Sn + 1 with partition q if and only if q covers p in Young's lattice. Iterating this procedure, one arrives at Young's semicanonical basis in the irreducible representation of Sn with partition p, which is indexed by the standard Young tableaux of shape p.
Read more about this topic: Young's Lattice
Famous quotes containing the word significance:
“History is the interpretation of the significance that the past has for us.”
—Johan Huizinga (1872–1945)
“Of what significance the light of day, if it is not the reflection of an inward dawn?—to what purpose is the veil of night withdrawn, if the morning reveals nothing to the soul? It is merely garish and glaring.”
—Henry David Thoreau (1817–1862)
“Politics is not an end, but a means. It is not a product, but a process. It is the art of government. Like other values it has its counterfeits. So much emphasis has been placed upon the false that the significance of the true has been obscured and politics has come to convey the meaning of crafty and cunning selfishness, instead of candid and sincere service.”
—Calvin Coolidge (1872–1933)