Tropical representations and identities of plactic monoids
- Date: Wednesday 11 December 2019, 16:00 – 17:00
- Location: Mathematics Level 8, MALL 1, School of Mathematics
- Type: Algebra, Logic and Algorithms, Seminars, Pure Mathematics
- Cost: Free
Mark Kambites, University of Manchester. Part of the Algebra, Logic, and Algorithms Seminar Series.
Plactic monoids are infinite, finitely generated monoids arising from a natural combinatorial multiplication on semistandard Young tableaux. Introduced by Knuth and first systematically studied by Lascoux and Schutzenberger, they have many applications in algebraic combinatorics. I shall discuss a recent discovery, made jointly with Marianne Johnson, of faithful representations of these monoids by matrices over the tropical semiring. The existence of such representations (which answers a question of Izhakian) implies that plactic monoids satisfy semigroup identities (which was a conjecture of Kubat and Okninski).