The Shifted Plactic Monoid

The shifted plactic monoid ( extended abstract )

The (shifted) plactic monoid. The celebrated Robinson-Schensted-Knuth correspondence (14) is a bijection between words in a linearly ordered alphabet X = {1 < 2 < 3 < · · · } and pairs of Young tableaux with entries in X . More precisely, each word corresponds to a pair consisting of a semistandard insertion tableau and a standard recording tableau. The words producing a given insertion tableau...

Finite convergent presentation of plactic monoid for type C

We give an explicit presentation for the plactic monoid for type C using admissible column generators. Thanks to the combinatorial properties of symplectic tableaux, we prove that this presentation is finite and convergent. We obtain as a corollary that plactic monoids for type C satisfy homological finiteness properties.

Schensted-Type correspondence, Plactic Monoid and Jeu de Taquin for type Cn

We use Kashiwara’s theory of crystal bases to study the plactic monoid for Uq(sp2n). Then we describe the corresponding insertion and sliding algorithms. The sliding algorithm is essentially the symplectic Jeu de Taquin defined by Sheats and our construction gives the proof of its compatibility with plactic relations.

The Plactic Monoid

Recognizable Subsets of the Two Letter Plactic Monoid

The plactic monoid P la(a, b) on two letters will be studied from the point of view of classical language theory. In particular, we will give the fine structure of its recognizable subsets.