Quantization of the rational spin Ruijsenaars-Schneider model via quantum Hamiltonian reduction

Lukas Hardi (U Hamburg and DESY)

Tuesday 25th November 12:00-13:00
Maths 110

Abstract

The rational spin Ruijsenaars–Schneider integrable model, whose classical equations of motion were introduced by Krichever and Zabrodin, describes N interacting relativistic particles, each carrying \ell internal spin degrees of freedom. In this talk, I will describe an approach of quantizing this model based on the method of quantum Hamiltonian reduction. By reducing the quantized cotangent bundle of GL_N with respect to a certain quantum moment map, one obtains the algebra of quantum observables of the rational spin Ruijsenaars–Schneider model. This algebra admits a geometric interpretation as a quantized quiver variety of the framed Jordan quiver. I will describe how loop algebra and Yangian symmetries of gl_\ell arise inside the algebra, how they control the integrable structure, and how they produce difference equations for eigenstates of the Hamiltonians. Time permitting, I will discuss evidence that the algebra becomes a shifted affine Yangian in the case of infinitely many particles.

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