25 citations · 225 across the 54 of their papers we have counts for
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Asymptotic Hecke algebras and Lusztig-Vogan bijection via affine matrix-ball construction
Dongkwan Kim, Pavlo Pylyavskyy
Affine matrix-ball construction (abbreviated AMBC) was developed by Chmutov, Lewis, Pylyavskyy, and Yudovina as an affine generalization of Robinson-Schensted correspondence. We sh…
Linear Laurent phenomenon algebras
Thomas Lam, Pavlo Pylyavskyy
In [LP] we introduced Laurent phenomenon algebras, a generalization of cluster algebras. Here we give an explicit description of Laurent phenomenon algebras with a linear initial s…
Laurent phenomenon algebras
Thomas Lam, Pavlo Pylyavskyy
We generalize Fomin and Zelevinsky's cluster algebras by allowing exchange polynomials to be arbitrary irreducible polynomials, rather than binomials.
Electrical networks and Lie theory
Thomas Lam, Pavlo Pylyavskyy
We introduce a new class of "electrical" Lie groups. These Lie groups, or more precisely their nonnegative parts, act on the space of planar electrical networks via combinatorial o…
Affine geometric crystals in unipotent loop groups
Thomas Lam, Pavlo Pylyavskyy
We study products of the affine geometric crystal of type A corresponding to symmetric powers of the standard representation. The quotient of this product by the R-matrix action is…