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A Young tableau (plural tableaux) is a method for decomposing products of an SU(N) group representation into a sum of irreducible representations. It provides the dimension and symmetry types of the irreducible representations, which is known as the Clebsch–Gordan series.
Consider the calculation of one of the character values for the symmetric group of order 8, when λ is the partition (5,2,1) and ρ is the partition (3,3,1,1). The shape partition λ specifies that the tableau must have three rows, the first having 5 boxes, the second having 2 boxes, and the third having 1 box.
In combinatorial mathematics, the hook length formula is a formula for the number of standard Young tableaux whose shape is a given Young diagram.It has applications in diverse areas such as representation theory, probability, and algorithm analysis; for example, the problem of longest increasing subsequences.
In mathematics, a Young tableau (/ t æ ˈ b l oʊ, ˈ t æ b l oʊ /; plural: tableaux) is a combinatorial object useful in representation theory and Schubert calculus.It provides a convenient way to describe the group representations of the symmetric and general linear groups and to study their properties.
For a field F, the generalized special unitary group over F, SU(p, q; F), is the group of all linear transformations of determinant 1 of a vector space of rank n = p + q over F which leave invariant a nondegenerate, Hermitian form of signature (p, q). This group is often referred to as the special unitary group of signature p q over F.
The Cayley table tells us whether a group is abelian. Because the group operation of an abelian group is commutative, a group is abelian if and only if its Cayley table's values are symmetric along its diagonal axis. The group {1, −1} above and the cyclic group of order 3 under ordinary multiplication are both examples of abelian groups, and ...
Created Date: 8/30/2012 4:52:52 PM
The group G has cohomological dimension less than or equal to n, denoted (), if the trivial -module R has a projective resolution of length n, i.e. there are projective-modules , …, and -module homomorphisms : (=, …,) and :, such that the image of coincides with the kernel of for =, …, and the kernel of is trivial.