Tropical Representations and Identities of Plactic Monoids

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).

Date and Venue

Start Date
Venue
Online Zoom meeting
End Date

Speaker

Mark Kambites

Speaker's Institution

University of Manchester

Files

Area

Semigroups, Automata and Languages

Financiamento