Seminar in Real and Complex Geometry

Monday, June 12, 2017, 17:00-18:00, Ornstein building, room 102

Zur Izhakian, University of Aberdeen

Tropical plactic algebra and semigroup representations


Tropical plactic algebra is a new algebra in which the Knuth relations are inferred from the underlying semiring structure. This algebra provides a natural framework for representations of the plactic monoid, and equivalently of Young tableaux, and its coarsening - the cloaktic monoid and the co-cloaktic monoid. Faithful representations of these coarse monoids by tropical matrices constitute tropical plactic algebras which are combined to a linear representation of the plactic monoid. These representations are utilized to prove the existence of nontrivial semigroup identities.