quantum-integrable-daha-dim

name	quantum-integrable-daha-dim
description	Quantum integrable systems from DAHA (Double Affine Hecke Algebra) and DIM (Ding-Iohara-Miki) algebra connections. Covers Macdonald polynomials, Koornwinder polynomials, Ruijsenaars systems, and type A vs type C system distinctions. Triggers: DAHA, DIM algebra, Macdonald polynomials, Koornwinder polynomials, Ruijsenaars system, quantum integrable systems, quantum toroidal algebra, type A system, type C system.
category	quantum-math

Quantum Integrable Systems from DAHA and DIM Algebra

Core Connections

DIM Algebra → Integrable Systems

• DIM (quantum toroidal algebra of gl_1) connects to quantum many-particle integrable systems
• Ruijsenaars trigonometric system as the typical example
• Eigenfunctions: Noumi-Shiraishi power series, Macdonald polynomials, Baker-Akhiezer functions

DAHA → DIM Correspondence

• Ruijsenaars Hamiltonians ↔ Cherednik DAHA Hamiltonians of type A
• DIM algebra ↔ spherical DAHA correspondence
• DAHA eigenfunctions = non-symmetric Macdonald polynomials

Type A vs Type C Distinctions

Type A

• Standard Ruijsenaars system
• Macdonald polynomials as eigenfunctions
• Non-symmetric Macdonald = DAHA eigenfunctions

Type C∨C

• Koornwinder Hamiltonians
• Symmetric Koornwinder polynomials as eigenfunctions
• Non-symmetric Koornwinder polynomials as DAHA eigenfunctions
• Generated from spherical version of type C∨C DAHA

Applications

1. Solving quantum integrable systems using DAHA/DIM algebra methods
2. Computing Macdonald and Koornwinder polynomials
3. Analyzing type A vs type C system differences
4. Twisted integrable systems construction