# 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…

## One Citation

Shifted quantum groups and matter multiplets in supersymmetric gauge theories

- Mathematics
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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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