Speaker
Arvind Ayyer, Indian Institute of Science
Abstract
I will first recall a natural multispecies variant of the inhomogeneous PushTASEP with site-dependent rates on the finite ring, where there is at most one particle per site. We have shown in earlier in joint work with James Martin and Lauren Williams that the stationary distribution of this process is proportional to the ASEP polynomials, introduced by Cantini, de Gier and Wheeler, at \(q =1\).
I will then describe joint work with Atsuo Kuniba (EJP, 2025) where we construct the generator of this process using the antisymmetric tensor representation of \(U_t(\widehat{sl}_{n+1})\). We then generalize this approach to construct the generator of a more general variant with arbitrary number of particles per site. We then derive the stationary probabilities using the so-called strange five-vertex model introduced by Kuniba, Okado and Scrimshaw, and show that the partition function is a certain plethysm of the Macdonald polynomial at \(q=1\). This is joint work with Atsuo Kuniba (arXiv:2602.17179).