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Award ID contains: 2204415

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  1. (, Selecta Mathematica)
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  2. ; ; (, Combinatorial Theory)
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  3. ; ; ; (, Annals of Combinatorics)
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  4. ; (, The Electronic Journal of Combinatorics)
    The up-operators $$u_i$$ and down-operators $$d_i$$ (introduced as Schur operators by Fomin) act on partitions by adding/removing a box to/from the $$i$$th column if possible. It is well known that the $$u_i$$ alone satisfy the relations of the (local) plactic monoid, and the present authors recently showed that relations of degree at most 4 suffice to describe all relations between the up-operators. Here we characterize the algebra generated by the up- and down-operators together, showing that it can be presented using only quadratic relations. 
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