Article
MSC:
05E05,
18A35,
18C15,
18D20,
18F30,
18M05,
18M80,
19A22,
20C30 | MR 4752517 | Zbl 1550.18004 | DOI: 10.21136/HS.2024.01
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Keywords:
categorification; lambda-ring; plethysm; Schur functor; symmetric function; symmetric group
categorification; lambda-ring; plethysm; Schur functor; symmetric function; symmetric group
Summary:
It is known that the Grothendieck ring of the category of Schur functors-or equivalently, the representation ring of the permutation groupoid-is the ring of symmetric functions. This ring has a rich structure, much of which is encapsulated in the fact that it is a 'plethory': a monoid in the category of birings with its substitution monoidal structure. We show that similarly the category of Schur functors is a '2-plethory', which descends to give the plethory structure on symmetric functions. Thus, much of the structure of symmetric functions exists at a higher level in the category of Schur functors.
References:
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