21 citations · 73 across the 20 of their papers we have counts for
12 papers · 1 filter
Scary Wheels (and Super Shrubs)
Andrei Neguţ, Alexander Tsymbaliuk
We prove the shuffle realization for quantum affine superalgebras of types in the loop realization, in that we construct an isomorphism between each of these algebras and a…
The loop-nilpotent cohomological Hall algebra
Shivang Jindal, Andrei Neguţ
We give an explicit shuffle algebra model for the loop-nilpotent cohomological Hall algebra (CoHA) of a tripled quiver with canonical cubic potential. As consequences, we (1) relat…
Fusion and specialization for type ADE shuffle algebras
Andrei Neguţ, Alexander Tsymbaliuk
Root vectors in quantum groups (of finite type) generalize to fused currents in quantum loop groups ([5]). In the present paper, we construct fused currents as duals to specializat…
Generators of the preprojective CoHA of a quiver
Andrei Neguţ
In this short note, we refine a result of Schiffmann-Vasserot, by showing that the localized preprojective cohomological Hall algebra of any quiver is spherical, i.e. generated by…
Quantum loop groups for symmetric Cartan matrices
Andrei Neguţ
We introduce a quantum loop group associated to a general symmetric Cartan matrix, by imposing just enough relations between the usual generators $\{e_{i,k}, f_{i,k}\}_{i \in I, k…
Shuffle algebras for quivers as quantum groups
Andrei Neguţ, Francesco Sala, Olivier Schiffmann
We define a quantum loop group associated to an arbitrary quiver and maximal set of deformation parameters, with generators indexed by $I \times \mathbb{…
Shuffle algebras for quivers and R-matrices
Andrei Neguţ
We define slope subalgebras in the shuffle algebra associated to a (doubled) quiver, thus yielding a factorization of the universal R-matrix of the double of the shuffle algebra in…
Quantum loop groups and shuffle algebras via Lyndon words
Andrei Neguţ, Alexander Tsymbaliuk
We study PBW bases of the untwisted quantum loop group (in the Drinfeld new presentation) using the combinatorics of loop words, by generalizing the treatment…
Deformed W-algebras in type A for rectangular nilpotent
Andrei Neguţ
For any natural numbers n,r, we construct an algebra P_n^r via generators and quadratic relations, and show that it deforms the W-algebra of gl_{nr} with respect to a nilpotent wit…
The q-AGT-W relations via shuffle algebras
Andrei Neguţ
We construct the action of the q-deformed W-algebra on its level r representation geometrically, using the moduli space of U(r) instantons on the plane and the double shuffle algeb…
Refined knot invariants and Hilbert schemes
Eugene Gorsky, Andrei Neguţ
We consider the construction of refined Chern-Simons torus knot invariants by M. Aganagic and S. Shakirov from the DAHA viewpoint of I. Cherednik. We give a proof of Cherednik's co…
Quantum toroidal and shuffle algebras
Andrei Neguţ
In this paper, we prove that the quantum toroidal algebra of gl_n is isomorphic to the double shuffle algebra of Feigin and Odesskii for the cyclic quiver. The shuffle algebra view…