Projective geometries, $Q$-polynomial structures, and quantum groups
Fuente:
arXiv
Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866913657843089408 |
|---|---|
| author | Terwilliger, Paul |
| author_facet | Terwilliger, Paul |
| contents | In 2023 we obtained a $Q$-polynomial structure for the projective geometry $L_N(q)$. In the present paper, we display a more general $Q$-polynomial structure for $L_N(q)$. Our new $Q$-polynomial structure is defined using a free parameter $φ$ that takes any positive real value. For $φ=1$ we recover the original $Q$-polynomial structure. We interpret the new $Q$-polynomial structure using the quantum group $U_{q^{1/2}}(\mathfrak{sl}_2)$ in the equitable presentation. We use the new $Q$-polynomial structure to obtain analogs of the four split decompositions that appear in the theory of $Q$-polynomial distance-regular graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_14964 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Projective geometries, $Q$-polynomial structures, and quantum groups Terwilliger, Paul Combinatorics Quantum Algebra 05E30 In 2023 we obtained a $Q$-polynomial structure for the projective geometry $L_N(q)$. In the present paper, we display a more general $Q$-polynomial structure for $L_N(q)$. Our new $Q$-polynomial structure is defined using a free parameter $φ$ that takes any positive real value. For $φ=1$ we recover the original $Q$-polynomial structure. We interpret the new $Q$-polynomial structure using the quantum group $U_{q^{1/2}}(\mathfrak{sl}_2)$ in the equitable presentation. We use the new $Q$-polynomial structure to obtain analogs of the four split decompositions that appear in the theory of $Q$-polynomial distance-regular graphs. |
| title | Projective geometries, $Q$-polynomial structures, and quantum groups |
| topic | Combinatorics Quantum Algebra 05E30 |
| url | https://arxiv.org/abs/2407.14964 |