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
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 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.
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