The conjugacy classes of nilpotent n × n matrices can be parametrised by partitions λ of n, and for a nilpotent η in the class parametrised by λ, the variety Fη of η-stable flags has its irreducible components parametrised by the standard Young tableaux of shape λ. We indicate how several algorithmic constructions defined for Young tableaux have significance in this context, thus extending Stei...

As is well known, Young diagrams consisting of n boxes parameterize isomorphism classes of finite-dimensional irreducible representations of the symmetric group Sn of degree n, and moreover the structure of each irreducible representation is described in terms of tableaux on the corresponding Young diagram; namely, a basis of the representation is labeled by standard tableaux, with which the ac...

This paper contains a short proof of a formula by Frame, Robinson, and Thrall [I] h h w ic counts the number of Young tableaux of a given shape. Let X = {X, >, X, > ..’ 2 X,} be a partition of R. The Ferrers diagram of h is an array of cells doubly indexed by pairs (i, j) with 1 < i < m, 1 <j < A( . A Young tableau of shape h (sometimes called a standard tableau) is an arrangement of the intege...

Recently the first author and Jang Soo Kim introduced lecture hall tableaux in their study of multivariate little q-Jacobi polynomials. They then enumerated bounded showed that enumeration is closely related to standard semistandard Young tableaux. In this paper we asymptotic behavior these thanks two other combinatorial models: non-intersecting paths on a graph whose faces are squares pentagon...

This paper gives a qualitative description how Young tableaux can be used to perform a Clebsch-Gordan decomposition of tensor products in SU(3) and how this can be generalized to SU(N).

We exhibit a weight-preserving bijection between semi-standard Young tableaux and skyline augmented fillings to provide the first combinatorial proof that the Schur functions decompose into nonsymmetric functions indexed by compositions. The insertion procedure involved in the proof leads to an analogue of the Robinson-SchenstedKnuth Algorithm for skyline augmented fillings. We also prove that ...

In this paper, we study the shape and reduced algebra for Lie superalgebra $${\mathfrak {sl}}(m,n)$$ . We define quasistandard Young tableaux, they give a combinatorial basis algebra, called diamond cone. There is natural bijective map from set of semistandard tableaux with $$\lambda $$ to smaller shape: cone compatible stratification algebra.

The hook-length formula is a well known result expressing the number of standard tableaux of shape λ in terms of the lengths of the hooks in the diagram of λ. Many proofs of this fact have been given, of varying complexity. We present here an elementary new proof which uses nothing more than the fundamental theorem of algebra. This proof was suggested by a q, t-analog of the hook formula given ...

We introduce a theory of jeu de taquin for increasing tableaux, extending fundamental work of [Schützenberger ’77] for standard Young tableaux. We apply this to give a new combinatorial rule for the K-theory Schubert calculus of Grassmannians via K-theoretic jeu de taquin, providing an alternative to the rules of [Buch ’02] and others. This rule naturally generalizes to give a conjectural root-...