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).

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-...

The number of standard Young tableaux of a fixed shape is famously given by the hook-length formula due to Frame, Robinson and Thrall. A bijective proof of Novelli, Pak and Stoyanovskii relies on a sorting algorithm akin to jeu-de-taquin which transforms an arbitrary filling of a partition into a standard Young tableau by exchanging adjacent entries. Recently, Krattenthaler and Müller defined t...

Ward identities of SUSY and R-symmetry relate n-point amplitudes in supersymmetric theories. We review recent work in which these Ward identities are solved in N = 4 SYM and N = 8 supergravity. The solution, valid at both tree and loop level, expresses any NMHV superamplitude in terms of a basis of ordinary amplitudes. Basis amplitudes are classified by semi-standard tableaux of rectangular N -...

The sl3 spider is a diagrammatic category used to study the representation theory of the quantum group Uq(sl3). The morphisms in this category are generated by a basis of non-elliptic webs. KhovanovKuperberg observed that non-elliptic webs are indexed by semistandard Young tableaux. They establish this bijection via a recursive growth algorithm. Recently, Tymoczko gave a simple version of this ...

Young’s lattice is the lattice of partitions of integers, ordered by inclusion of diagrams. Standard Young tableaux can be represented as paths in Young’s lattice that go up by one square at each step, and more general paths in Young’s lattice correspond to more general kinds of tableaux. Using the theory of symmetric functions, in particular Pieri’s rule for multiplying a Schur function by a c...