Richard P. Stanley Seminar in Combinatorics: A diagrammatic realization of the Okada algebra

SEMINARS, HARVARD-MIT COMBINATORICS

Speaker:

Jeanne Scott - Brandeis

It is well known that the Young lattice is the Bratelli diagram of the symmetric groups, expressing how irreducible representations restrict from S(n) to S(n-1).  In 1975 Stanley discovered a similar lattice called the Young-Fibonacci lattice which was later realized as the Bratelli diagram of a family of algebras by Okada in 1994. In joint work with Florent Hivert (Université Paris-Sud) we realize the n-th Okada algebra as a diagram algebra with a multiplicative/monoid basis consisting of n-strand Temperley-Lieb diagrams, each equipped with a "height" labeling of its strands. The proof involves a diagrammatic version of Fomin's Robinson-Schensted correspondence for the Young-Fibonacci lattice. This basis is cellular, which affords us with a novel, diagrammatic presentation of the irreducible representations of the Okada algebra (i.e. cell modules).

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