Representations of Multiparameter Quantum Groups
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909170407571456 |
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| author | Dobrev, V. K. |
| author_facet | Dobrev, V. K. |
| contents | We construct representations of the quantum algebras ~$U_{q{\bf q}}(gl(n))$ and ~$U_{q{\bf q}}(sl(n))$~ which are in duality with the multiparameter quantum groups ~$GL_{q{\bf q}}(n)$, ~$SL_{q{\bf q}}(n)$,~ respectively. These objects depend on ~$n(n-1)/2+1$~ deformation parameters ~$q,q_{ij}$ ($1\leq i <j\leq n$) which is the maximal possible number in the case of $GL(n)$. The representations are labelled by $n-1$ complex numbers ~$r_i$~ and are acting in the space of formal power series of ~$n(n-1)/2$~ non-commuting variables. These variables generate quantum flag manifolds of ~$GL_{q{\bf q}}(n)$, ~$SL_{q{\bf q}}(n)$. The case $n=3$ is treated in more detail. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_09843 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Representations of Multiparameter Quantum Groups Dobrev, V. K. Mathematical Physics High Energy Physics - Theory Quantum Algebra Representation Theory We construct representations of the quantum algebras ~$U_{q{\bf q}}(gl(n))$ and ~$U_{q{\bf q}}(sl(n))$~ which are in duality with the multiparameter quantum groups ~$GL_{q{\bf q}}(n)$, ~$SL_{q{\bf q}}(n)$,~ respectively. These objects depend on ~$n(n-1)/2+1$~ deformation parameters ~$q,q_{ij}$ ($1\leq i <j\leq n$) which is the maximal possible number in the case of $GL(n)$. The representations are labelled by $n-1$ complex numbers ~$r_i$~ and are acting in the space of formal power series of ~$n(n-1)/2$~ non-commuting variables. These variables generate quantum flag manifolds of ~$GL_{q{\bf q}}(n)$, ~$SL_{q{\bf q}}(n)$. The case $n=3$ is treated in more detail. |
| title | Representations of Multiparameter Quantum Groups |
| topic | Mathematical Physics High Energy Physics - Theory Quantum Algebra Representation Theory |
| url | https://arxiv.org/abs/2404.09843 |