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Abstract: |
Masaki Kashiwara, a recipient of Kyoto prize and Chern medal this year, invented Kashiwara crystal in early 1990’s. In type A, highest weight crystals give Schur polynomials as their characters. A Schur positive polynomial is a symmetric polynomial with integral coefficients which admits expression as (positive) sum of Schur polynomials. For a Schur positive polynomial, we may expect that there exists a crystal whose character is the given polynomial such that an isomorphism of crystals explains the identity that it is equal to sum of Schur polynomials. We give several examples of this kind. They include those using ghost leg or grid class.
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