• Corpus ID: 238856820

Shuffle algebras, lattice paths and the commuting scheme

  title={Shuffle algebras, lattice paths and the commuting scheme},
  author={Alexandr Garbali and Paul Zinn-Justin},
The commutative trigonometric shuffle algebra A is a space of symmetric rational functions satisfying certain wheel conditions [FO97, FHH09]. We describe a ring isomorphism between A and the center of the Hecke algebra using a realization of the elements of A as partition functions of coloured lattice paths associated to the R-matrix of U t1/2(ĝl∞). As an application, we compute under certain conditions the Hilbert series of the commuting scheme and identify it with a particular element of the…