Alexander M. Kuznetsov

activity

19972022

most citedA note on the symplectic structure on the space of G-monopoles

33 citations · 40 across the 9 of their papers we have counts for

collaborators

9 papers

math.CV2022

Systems biorthogonal to exponential systems on a finite union of intervals

Anton Baranov, Yurii Belov, Alexander Kuznetsov

We study the properties of a system biorthogonal to a complete and minimal system of exponentials in $L^{2} (E)$ , where $E$ is a finite union of intervals, and show that in the case w…

math.AG2015

Intersection cohomology of the Uhlenbeck compactification of the Calogero-Moser space

Michael Finkelberg, Victor Ginzburg, Andrei Ionov +1

We study the natural Gieseker and Uhlenbeck compactifications of the rational Calogero-Moser phase space. The Gieseker compactification is smooth and provides a small resolution of…

math.AG2015★ 4 cited

Towards a cluster structure on trigonometric zastava

Michael Finkelberg, Alexander Kuznetsov, Leonid Rybnikov +1

We study a moduli problem on a nodal curve of arithmetic genus 1, whose solution is an open subscheme in the zastava space for projective line. This moduli space is equipped with a…

math.AG2002★ 2 cited

Uhlenbeck spaces for $A^{2}$ and affine Lie algebra $s l^_{n}$

Michael Finkelberg, Dennis Gaitsgory, Alexander Kuznetsov

We introduce an Uhlenbeck closure of the space of based maps from projective line to the Kashiwara flag scheme of an untwisted affine Lie algebra. For the algebra $s l^_{n}$ this…

math.AG1999

Parabolic sheaves on surfaces and affine Lie algebra $g l^_{n}$

Michael Finkelberg, Alexander Kuznetsov

We give an example of geometric construction (via Hecke correspondences) of certain representations of the affine Lie algebra $g l^_{n}$ . The construction is similar to the one o…

math.AG1998★ 33 cited

A note on the symplectic structure on the space of G-monopoles

Michael Finkelberg, Alexander Kuznetsov, Nikita Markarian +1

Let $G$ be a semisimple complex Lie group with a Borel subgroup $B$ . Let $X = G / B$ be the flag manifold of $G$ . Let $C = P^{1} ∋ \infty$ be the projective line. Let $α\in H_2(X,{\Bbb Z})…

alg-geom1997

Semiinfinite Flags. II. Local and Global Intersection Cohomology of Quasimaps' Spaces

Boris Feigin, Michael Finkelberg, Alexander Kuznetsov +1

For a simple algebraic group $G$ we study the space $Q$ of Quasimaps from the projective line $C$ to the flag variety of $G$ . We prove that the global Intersection Cohomology of $Q…

alg-geom1997★ 1 cited

The Singular Supports of IC sheaves on Quasimaps' Spaces are Irreducible

Michael Finkelberg, Alexander Kuznetsov, Ivan Mirković

Let $C$ be a smooth projective curve of genus 0. Let $B$ be the variety of complete flags in an $n$ -dimensional vector space $V$ . Given an $(n - 1)$ -tuple $α \in N [I]$ of positive int…