Computing Young's Natural Representations for Generalized Symmetric Groups
| Autor: | Paul, Koushik, Pfeiffer, Götz |
|---|---|
| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We provide an algorithmic framework for the computation of explicit representing matrices for all irreducible representations of a generalized symmetric group $\Grin_n$, i.e., a wreath product of cyclic group of order $r$ with the symmetric group $\Symm_n$. The basic building block for this framework is the Specht matrix, a matrix with entries $0$ and $\pm1$, defined in terms of pairs of certain words. Combinatorial objects like Young diagrams and Young tableaus arise naturally from this setup. In the case $r = 1$, we recover Young's natural representations of the symmetric group. For general $r$, a suitable notion of pairs of $r$-words is used to extend the construction to generalized symmetric groups. Separately, for $r = 2$, where $\Grin_n$ is the Weyl group of type $B_n$, a different construction is based on a notion of pairs of biwords. Comment: 18 pages. Comments welcome |
| Databáze: | arXiv |
| Externí odkaz: |
|