@article{Wang2023, 
author = {Wanxia Wang and Shilin Yang},
title = {On finite-dimensional irreducible modules for the universal Askey-Wilson algebra},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {8},
pages = {18930-18947},
keywords = {universal Askey-Wilson algebra, irreducible module, Verma module},
url = {https://www.sciopen.com/article/10.3934/math.2023964},
doi = {10.3934/math.2023964},
abstract = {Let        Δ    q   be the universal Askey-Wilson algebra. If    q is not a root of unity, it is shown in the Huang's earlier paper that an    (  n  +  1  )-dimensional irreducible        Δ    q  -module is a quotient        V    n    (  a  ,  b  ,  c  ) of a        Δ    q  -Verma module with               C      o      n      d      i      t      i      o      n      A      :          a  b  c  ,      a          −      1        b  c  ,  a      b          −      1        c  ,  a  b      c          −      1        ∉      {                  q                  n          −          2          i          +          1                            |            1      ≤      i      ≤      n        }    .The aim of this paper is to discuss the structures of    (  n  +  1  )-dimensional        Δ    q  -modules        V    n    (  a  ,  b  ,  c  ) when the given triples    (  a  ,  b  ,  c  ) do not satisfy Condition A.}
}