Quantum Harish-Chandra isomorphism for the double affine Hecke algebra of GL n

Key Points

• The central aim is to establish an isomorphism involving the spherical double affine Hecke algebra for GLn under generic parameters.
• Proving the quantum radial parts map of Varagnolo and Vasserot.
• Applying algebraic techniques related to double affine Hecke algebras.
• Using definitions and properties of quiver varieties as introduced by Jordan.
• Demonstrated an isomorphism between the spherical double affine Hecke algebra of GLn and a quantized multiplicative quiver variety.
• Showed this holds true for generic parameters, broadening the implications of the isomorphism.