Tableaux have long been used to study combinatorial properties of permutations and multiset permutations. Discovered independently by Robinson and Schensted and generalized by Knuth, the Robinson-Schensted correspondence has provided a fundamental tool for relating permutations to tableaux. In 1963, Schützenberger defined a process called evacuation on standard tableaux which gives a relationsh...

We study a particular class of infinite-dimensional representations $\mathfrak{osp}(1|2n)$. These $L_n(p)$ are characterized by positive integer $p$, and the lowest component in $p$-fold tensor product metaplectic representation construct new polynomial basis for arising from embedding $\mathfrak{osp}(1|2np) \supset \mathfrak{osp}(1|2n)$. The vectors labelled semi-standard Young tableaux, expre...

We deene an action of the symmetric group S n 2 ] on the set of domino tableaux, and prove that the number of domino tableaux of weight 0 does not depend on the permutation of the weight 0. A bijective proof of the well-known result due to J. Stembridge that the number of self{evacuating tableaux of a given shape and weight = (1 ; : : : ; n+1 2 ] ; n 2 ] ; : : : ; 1), is equal to that of domino...

For a semisimple Lie algebra g the orbit method attempts to assign representations of g to (coadjoint) orbits in g∗. Orbital varieties are particular Lagrangian subvarieties of such orbits leading to highest weight representations of g. In sln orbital varieties are described by Young tableaux. In this paper we consider so called Richardson orbital varieties in sln. A Richardson orbital variety ...

We establish the existence of an involution on tabloids that is analogous to Schützenberger’s evacuation map standard Young tableaux. find number its fixed points given by evaluating a certain Green’s polynomial at $$q = -1$$ , and satisfies “domino-like” recurrence relation.

Abstract. We introduce an infinite family of lower triangular matrices Γ(s), where γ (s) n,i counts the standard Young tableaux on n cells, with at most s columns, whose second and third column lengths differ by i. We show that the entries of these matrices satisfy a three-term row recurrence and we deduce recursive and asymptotic properties for the total number τs(n) of tableaux on n cells and...

In combinatorics there is a well-known duality between non-nesting and non-crossing objects. In algebra there are many objects which are standard, for example Standard Young Tableaux, Standard Monomials, Standard Bitableaux. We adopt a point of view that these standard objects are really non-nesting, and we find their non-crossing counterparts.