| Title:
|
Schur Functors and Categorified Plethysm (English) |
| Author:
|
Baez, John C. |
| Author:
|
Moeller, Joe |
| Author:
|
Trimble, Todd |
| Language:
|
English |
| Journal:
|
Higher Structures |
| ISSN:
|
2209-0606 |
| Volume:
|
8 |
| Issue:
|
1 |
| Year:
|
2024 |
| Pages:
|
1-53 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| Keyword:
|
categorification |
| Keyword:
|
lambda-ring |
| Keyword:
|
plethysm |
| Keyword:
|
Schur functor |
| Keyword:
|
symmetric function |
| Keyword:
|
symmetric group |
| MSC:
|
05E05 |
| MSC:
|
18A35 |
| MSC:
|
18C15 |
| MSC:
|
18D20 |
| MSC:
|
18F30 |
| MSC:
|
18M05 |
| MSC:
|
18M80 |
| MSC:
|
19A22 |
| MSC:
|
20C30 |
| idZBL:
|
Zbl 1550.18004 |
| idMR:
|
MR4752517 |
| DOI:
|
10.21136/HS.2024.01 |
| . |
| Date available:
|
2026-03-13T14:04:06Z |
| Last updated:
|
2026-03-13 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/153465 |
| . |
| Reference:
|
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