29 citations · 72 across the 12 of their papers we have counts for
9 papers · 1 filter
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)…
On a conjecture of Khoroshkin and Tolstoy
Andrea Appel, Sachin Gautam, Curtis Wendlandt
We prove a no-go theorem on the factorization of the lower triangular part in the Gaussian decomposition of the Yangian's universal -matrix, yielding a negative answer to a conj…
Quantization of continuum Kac-Moody algebras
Andrea Appel, Francesco Sala
Continuum Kac-Moody algebras have been recently introduced by the authors and O. Schiffmann. These are Lie algebras governed by a continuum root system, which can be realized as un…
A DG-extension of symmetric functions arising from higher representation theory
Andrea Appel, Ilknur Egilmez, Matthew Hogancamp +1
We investigate analogs of symmetric functions arising from an extension of the nilHecke algebra defined by Naisse and Vaz. These extended symmetric functions form a subalgebra of t…
A 2-categorical extension of Etingof-Kazhdan quantisation
Andrea Appel, Valerio Toledano-Laredo
Let k be a field of characteristic zero. Etingof and Kazhdan constructed a quantisation U_h(b) of any Lie bialgebra b over k, which depends on the choice of an associator Phi. They…
Coxeter categories and quantum groups
Andrea Appel, Valerio Toledano-Laredo
We define the notion of braided Coxeter category, which is informally a tensor category carrying compatible, commuting actions of a generalised braid group B_W and Artin's braid gr…
Monodromy of the Casimir connection of a symmetrisable Kac-Moody algebra
Andrea Appel, Valerio Toledano-Laredo
Let g be a symmetrisable Kac-Moody algebra and V an integrable g-module in category O. We show that the monodromy of the (normally ordered) rational Casimir connection on V can be…
Uniqueness of Coxeter structures on Kac-Moody algebras
Andrea Appel, Valerio Toledano-Laredo
Let g be a symmetrisable Kac-Moody algebra, and U_h(g) the corresponding quantum group. We showed in arXiv:1610.09744 and arXiv:1610.09741 that the braided quasi-Coxeter structure…
Quasi-Coxeter categories and a relative Etingof-Kazhdan quantization functor
Andrea Appel, Valerio Toledano-Laredo
Let g be a symmetrizable Kac-Moody algebra and U_h(g) its quantized enveloping algebra. The quantum Weyl group operators of U_h(g) and the universal R-matrices of its Levi subalgeb…