The Knuth bijection, quantum matrices and free crystals
Arkady Berenstein
Cornell University
Febrary 17,
4:15pm
refreshments at 3:45pm
2338
ABSTRACT

We explicitly compute the celebrated RobinsonSchenstedKnuth
correspondence (RSK) between the set of the matrices with nonnegative
integer entries, and the set of the plane partitions.
More precisely, in suitable linear coordinates on both sets, the RSK is
expressed via minima of linear forms, i.e, in the piecewiselinear terms.
In particular, we answer the following question by Curtis Grene: ``What
shape corresponds to a given permutation under the Robinson
correspondence? Our main tool in establishing these formulas is the quantum
matrices and crystal bases. Based on the ideas of M. Kashiwara, we
introduce the notion of free crystals, and build two such crystals on the
set of all matrices with integer entries. The RSK is completely described
as a canonical isomorphism between these two crystals.

Speaker's Contact Info: arkady(atsign)math.cornell.edu
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