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Andrei Negut

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Publications associées (6)

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AN INTEGRAL FORM OF QUANTUM TOROIDAL gl1

Andrei Negut

We consider the (direct sum over all n ∈ ℕ of the) K-theory of the semi-nilpotent commuting variety of gln, and describe its convolution algebra structure in two ways: the first as an explicit shuffle algebra (i.e., a particular ℤ[q1±1, q2±1]-submodule of ...

2024

Hecke categories, idempotents, and commuting stacks

Andrei Negut

We formulate a connection between a topological and a geometric category. The former is the idempotent completion of the (horizontal) trace of the affine Hecke category, while the latter is the equivariant derived category of the (semi-nilpotent) commuting ...

SPRINGER HEIDELBERG2025

Quantum loop groups for arbitrary quivers

Andrei Negut

We study the dual constructions of quantum loop groups and Feigin-Odesskii type shuffle algebras for an arbitrary quiver, for which the arrow parameters are arbitrary non-zero elements of any field. Examples of our setup include K-theoretic Hall algebras o ...

American Mathematical Society2025

Generators of the preprojective CoHA of a quiver

Andrei Negut

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, that is, generated by elements of minimal dimension. ...

Wiley2025

REDUCED QUIVER QUANTUM TOROIDAL ALGEBRAS

Andrei Negut

We give a generators-and-relations description of the reduced versions of quiver quantum toroidal algebras, which act on the spaces of BPS states associated to (noncompact) toric Calabi-Yau threefolds X. As an application, we obtain a description of the K- ...

Cambridge University Press2025

Quantum loop groups and K$K$‐theoretic stable envelopes

Andrei Negut

We develop the connection between the preprojective ‐theoretic Hall algebra [Schiffmann and Vasserot (Duke Math. J. 162 (2013), no. 2, 279–366), Yang and Zhao (Proc. London Math. Soc. (3) 116 (2018), no. 5, 1029–1074)] of a quiver and the quantum loop grou ...

Wiley2025