$k$-partial permutations and the center of the wreath product $\mathcal{S}_k\wr \mathcal{S}_n$ algebra
| Autor: | Omar Tout |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Algebra and Number Theory
Center (category theory) Structure (category theory) Symmetric function Combinatorics Algebra 05E05 05E10 05E15 20C30 Integer Wreath product FOS: Mathematics Discrete Mathematics and Combinatorics Universal algebra Mathematics - Combinatorics Combinatorics (math.CO) Algebra over a field Representation Theory (math.RT) Mathematics - Representation Theory Mathematics |
| Popis: | We generalize the concept of partial permutations of Ivanov and Kerov and introducek-partial permutations. This allows us to show that the structure coefficients of the center of the wreath product$${\mathcal {S}}_k\wr {\mathcal {S}}_n$$Sk≀Snalgebra are polynomials innwith nonnegative integer coefficients. We use a universal algebra$${\mathcal {I}}_\infty ^k$$I∞k, which projects on the center$$Z({\mathbb {C}}[{\mathcal {S}}_k\wr {\mathcal {S}}_n])$$Z(C[Sk≀Sn])for eachn. We show that$${\mathcal {I}}_\infty ^k$$I∞kis isomorphic to the algebra of shifted symmetric functions on many alphabets. |
| Databáze: | OpenAIRE |
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