Plactic relations for $r$-domino tableaux

Some bijective correspondences involving domino tableaux

We define a number of new combinatorial operations on skew semistandard domino tableaux, which together with constructions introduced earlier by C. Carre and B. Leclerc, define an elegant structure on the set of these tableaux, that closely parallels the structure defined in [math.CO/9908099] for ordinary skew semistandard tableaux, that is related to the Littlewood-Richardson rule. These operations are: (1) a bijection between semistandard domino tableaux and certain pairs of ordinary tableaux of the same weight that together fill the same shape; (2) a weight preserving transformation of domi…

A family of operators generating domino tableaux of a fixed shape and a decomposition of left cells into isotypic components

We exhibit a set of operators on pairs of domino tableaux of the same shape sending them to other such pairs with the same right tableau, in such a way that any two pairs with the same right tableau are conjugate by some composition of the operators. Using these operators we give explicit bases for the isotypic components of a classical Kazhdan-Lusztig left cell in terms of Kazhdan-Lusztig basis vectors.

Components of the Springer Fiber and Domino Tableaux

Consider a complex classical semi-simple Lie group along with the set of its nilpotent coadjoint orbits. When the group is of type A, the set of orbital varieties contained in a given nilpotent orbit is described a set of standard Young tableaux. We parameterize both, the orbital varieties and the irreducible components of unipotent varieties in the other classical groups by sets of standard domino tableaux. The main tools are Spaltenstein's results on signed domino tableaux together with Garfinkle's operations on standard domino tableaux.

Super RSK-algorithms and super plactic monoid

We construct the analogue of the plactic monoid for the super semistandard Young tableaux over a signed alphabet. This is done by developing a generalization of the Knuth's relations. Moreover we get generalizations of Greene's invariants and Young-Pieri rule. A generalization of the symmetry theorem in the signed case is also obtained. Except for this last result, all the other results are proved without restrictions on the orderings of the alphabets.

0-Hecke 模、多米诺骨牌表与 B 型拟对称函数

0-Hecke Modules, Domino Tableaux, and Type-$B$ Quasisymmetric Functions

本文将升序相容推广至所有 Coxeter 群以构造 0-Hecke 模，并在 B 型中解释拟对称、峰函数及移位多米诺函数，证明正展开与限制特征公式。

A plactic algebra of extremal weight crystals and the Cauchy identity for Schur operators

We give a new bijective interpretation of the Cauchy identity for Schur operators which is a commutation relation between two formal power series with operator coefficients. We introduce a plactic algebra associated with the Kashiwara's extremal weight crystals over the Kac-Moody algebra of type $A_{+\infty}$, and construct a Knuth type correspondence preserving the plactic relations. This bijection yields the Cauchy identity for Schur operators as a homomorphic image of its associated identity for plactic characters of extremal weight crystals, and also recovers the Sagan and Stanley's corres…