Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2022
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2209.03531 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913259046567936 |
|---|---|
| author | Franceschini, Chiara Kuan, Jeffrey Zhou, Zhengye |
| author_facet | Franceschini, Chiara Kuan, Jeffrey Zhou, Zhengye |
| contents | We propose a novel, general method to produce orthogonal polynomial dualities from the $^*$--bialgebra structure of Drinfeld--Jimbo quantum groups. The $^*$--structure allows for the construction of certain \textit{unitary} symmetries, which imply the orthogonality of the duality functions. In the case of the quantum group $\mathcal{U}_q(\mathfrak{gl}_{n+1})$, the result is a nested multivariate $q$--Krawtchouk duality for the $n$--species ASEP$(q,\boldsymbolθ)$. The method also applies to other quantized simple Lie algebras and to stochastic vertex models.
As a probabilistic application of the duality relation found, we provide the explicit formula of the $q-$shifted factorial moments (namely the $q$-analogue of the Pochhammer symbol) for the two--species $q$--TAZRP (totally asymmetric zero range process). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_03531 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Orthogonal polynomial duality and unitary symmetries of multi--species ASEP$(q,\boldsymbolθ)$ and higher--spin vertex models via $^*$--bialgebra structure of higher rank quantum groups Franceschini, Chiara Kuan, Jeffrey Zhou, Zhengye Probability 60K35 We propose a novel, general method to produce orthogonal polynomial dualities from the $^*$--bialgebra structure of Drinfeld--Jimbo quantum groups. The $^*$--structure allows for the construction of certain \textit{unitary} symmetries, which imply the orthogonality of the duality functions. In the case of the quantum group $\mathcal{U}_q(\mathfrak{gl}_{n+1})$, the result is a nested multivariate $q$--Krawtchouk duality for the $n$--species ASEP$(q,\boldsymbolθ)$. The method also applies to other quantized simple Lie algebras and to stochastic vertex models. As a probabilistic application of the duality relation found, we provide the explicit formula of the $q-$shifted factorial moments (namely the $q$-analogue of the Pochhammer symbol) for the two--species $q$--TAZRP (totally asymmetric zero range process). |
| title | Orthogonal polynomial duality and unitary symmetries of multi--species ASEP$(q,\boldsymbolθ)$ and higher--spin vertex models via $^*$--bialgebra structure of higher rank quantum groups |
| topic | Probability 60K35 |
| url | https://arxiv.org/abs/2209.03531 |