Twisted Cherednik Systems and Non-symmetric Macdonald Polynomials
Published:Dec 31, 2025 11:56
•1 min read
•ArXiv
Analysis
This paper explores eigenfunctions of many-body system Hamiltonians related to twisted Cherednik operators, connecting them to non-symmetric Macdonald polynomials and the Ding-Iohara-Miki (DIM) algebra. It offers a new perspective on integrable systems by focusing on non-symmetric polynomials and provides a formula to construct eigenfunctions from non-symmetric Macdonald polynomials. This work contributes to the understanding of integrable systems and the relationship between different mathematical objects.
Key Takeaways
- •Explores eigenfunctions of many-body system Hamiltonians related to twisted Cherednik operators.
- •Connects these eigenfunctions to non-symmetric Macdonald polynomials and the DIM algebra.
- •Offers a new perspective on integrable systems by focusing on non-symmetric polynomials.
- •Provides a formula to construct eigenfunctions from non-symmetric Macdonald polynomials.
Reference
“The eigenfunctions admit an expansion with universal coefficients so that the dependence on the twist $a$ is hidden only in these ground state eigenfunctions, and we suggest a general formula that allows one to construct these eigenfunctions from non-symmetric Macdonald polynomials.”