Matrix‐Valued Cauchy Bi‐Orthogonal Polynomials and a Novel Noncommutative Integrable Lattice
ABSTRACT Matrix‐valued Cauchy bi‐orthogonal polynomials are proposed in this paper, together with its quasideterminant expression. It is shown that the coefficients in the four‐term recurrence relation for matrix‐valued Cauchy bi‐orthogonal polynomials satisfy a novel noncommutative integrable system, whose Lax pair is given by fractional differential operators with non‐abelian variables.
Authors
- Ying Shi
- Guo‐Fu Yu
- Shi‐Hao Li (ORCID: https://orcid.org/0000-0003-2510-4079)
- Jun‐Xiao Zhao
Institutions
- Zhejiang University of Science and Technology (CN)
- Shanghai Jiao Tong University (CN)
- Sichuan University (CN)
- University of Glasgow (GB)
Publication Details
- Journal
- Studies in Applied Mathematics
- Published
- 2025-03-01
- DOI
- https://doi.org/10.1111/sapm.70040
- Citations
- 2
- Primary Topic
- Mathematical functions and polynomials
- Type
- article
- Field-Weighted Citation Impact
- 7.45
Funders
- National Natural Science Foundation of China