• Corpus ID: 238856820

Shuffle algebras, lattice paths and the commuting scheme

@inproceedings{Garbali2021ShuffleAL,
  title={Shuffle algebras, lattice paths and the commuting scheme},
  author={Alexandr Garbali and Paul Zinn-Justin},
  year={2021}
}
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… 
Shifted quantum groups and matter multiplets in supersymmetric gauge theories
The notion of shifted quantum groups has recently played an important role in algebraic geometry. This subtle modification of the original definition brings more flexibility in the representation theory

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