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

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…

Plactic relations for $r$-domino tableaux

The work of C. Bonnaf{é}, M. Geck, L. Iancu and T. Lam \cite{Geck-Lam} shows through two conjectures that $r$-domino tableaux have an important role in Kazhdan-Lusztig theory of type $B$ with unequal parameters. In this paper we provide plactic relations on signed permutations which determine whether given two signed permutations have the same insertion $r$-domino tableaux in Garfinkle's algorithm \cite{Garfinkle1}.

Isotypic components in type $D$

We extend the result of our earlier paper "A family of operators generating domino tableaux..." to type $D$, showing that the same recipe holds for computing basis vectors of isotypic components of Kazhdan-Lusztig cells in that type.

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.

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 Sundaram type bijection for SO(3): vacillating tableaux and pairs of standard Young tableaux and orthogonal Littlewood-Richardson tableaux

Based on the direct-sum-decomposition of the rth tensor power of the defining representation of the special orthogonal group SO(2k+1) one is interested in a bijective approach for determining the Frobenius characters of the isotypic components. In particular this leads us to a bijection between vacillating tableaux and pairs of standard Young tableaux and orthogonal Littlewood-Richardson tableaux, which we present for SO(3). Moreover we introduce the descent set of a vacillating tableau. As our bijection preserves this descent set, we also obtain the quasi-symmetric expansion of the Frobenius …