101 citations · 272 across the 18 of their papers we have counts for
15 papers · 1 filter
An abelian formula for the quantum Weyl group action of the coroot lattice
S. Gautam, V. Toledano-Laredo
Let g be a complex simple Lie algebra and Uq(Lg) its quantum loop algebra, where q is not a root of unity. We give an explicit formula for the quantum Weyl group action of the coro…
Pure braid group actions on category O modules
Andrea Appel, Valerio Toledano-Laredo
Let g be a symmetrisable Kac-Moody algebra and U_h(g) its quantised enveloping algebra. Answering a question of P. Etingof, we prove that the quantum Weyl group operators of U_h(g)…
The elliptic Casimir connection of a simple Lie algebra
Valerio Toledano-Laredo, Yaping Yang
We construct a flat connection on the elliptic configuration space associated to any complex semisimple Lie algebra g. This elliptic Casimir connection has logarithmic singularitie…
Elliptic quantum groups and their finite-dimensional representations
Sachin Gautam, Valerio Toledano-Laredo
Let g be a complex semisimple Lie algebra, tau a point in the upper half-plane, and h a complex deformation parameter such that the image of h in the elliptic curve E_tau is of inf…
Quasi-Coxeter quasitriangular quasibialgebras and the Casimir connection
Valerio Toledano-Laredo
Let g be a complex, semisimple Lie algebra. We prove the existence of a quasi-Coxeter, quasitriangular quasibialgebra structure on the enveloping algebra of g, which binds the quas…
Yangians, quantum loop algebras and abelian difference equations
S. Gautam, V. Toledano-Laredo
Let g be a complex, semisimple Lie algebra, and Y_h(g) and U_q(Lg) the Yangian and quantum loop algebra of g. Assuming that h is not a rational number and that q=exp(i πh), we cons…