Abstract
We find a semigroup Qn, whose category of partial representations contains the representation category Rep(Fn) of the free left regular band Fn. We use this to construct a resolution for the absolute kernel of a representation of Fn, for which the kernel Spn of the Markov operation in the Tsetlin library model is a prominent example. We obtain a formula for the dimension of the absolute kernel, generalizing the equality of the dimension of Spn to the number of derangements of order n.
| Original language | English |
|---|---|
| Pages (from-to) | 37-62 |
| Number of pages | 26 |
| Journal | International Journal of Algebra and Computation |
| Volume | 31 |
| Issue number | 1 |
| DOIs | |
| State | Published - Feb 2021 |
Bibliographical note
Publisher Copyright:© 2021 World Scientific Publishing Company.
Funding
We thank Stuart Margolis, Ron Adin, and Yuval Roichman, for their helpful comments. This work was supported by the Israel science foundation grant #1623/16.
| Funders | Funder number |
|---|---|
| Israel Science Foundation | 1623/16 |
Keywords
- Left regular bands
- Tsetlin library
- coherent systems of polynomials
- inclusion-exclusion
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