Seminar in Real and Complex Geometry
Monday, June 12, 2017, 17:0018:00,
Ornstein building, room 102
Zur Izhakian, University of Aberdeen
Tropical plactic algebra and semigroup representations
Abstract
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 cocloaktic 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.
