8 papers
Helly Numbers for Connected Reductive Groups and Splitting of Toric Principal Bundles
Boris Tsvelikhovskiy
For an almost simple complex algebraic group of semisimple rank , we prove that a finite family of parabolic subgroups contains a common maximal torus whenever every subfami…
Notes from a family of smooth -Hilbert schemes
Boris Tsvelikhovskiy
Let be the cyclic group of order , and let denote a primitive th root of unity. Consider the action of on $\mathbb{C…
On a Dichotomy for Skyscraper Sheaves under the Bridgeland-King-Reid Equivalence
Boris Tsvelikhovskiy
Let be a finite abelian subgroup, and let be the corresponding -Hilbert scheme. Denote by $Ψ: D^b…
Toric vector bundles over a discrete valuation ring and Bruhat-Tits buildings
Kiumars Kaveh, Christopher Manon, Boris Tsvelikhovskiy
We give a classification of rank torus equivariant vector bundles on a toric scheme over a discrete valuation ring , in terms of grade…
The universe inside Hall algebras of coherent sheaves on toric resolutions
Boris Tsvelikhovskiy
Let be a simple Lie algebra of type with the corresponding affine Kac-Moody algebra and $\mathfrak{n}_-\subset \…
On Poincare polynomials of shuffle algebra representations
Boris Tsvelikhovskiy
In this paper we study some combinatorial properties of the shuffle algebra with two complex parameters and, in particular, obtain the Hilbert series for $S_{q_{1…
On categories of quiver varieties overlying the bouquet graphs
Boris Tsvelikhovskiy
We study representation theory of quantizations of Nakajima quiver varieties associated to bouquet quivers. We show that there are no finite dimensional representations of the quan…
Nontrivial Topological Quandles
Boris Tsvelikhovskiy
We show that there are infinitely many nonisomorphic quandle structures on any topogical space of positive dimension. In particular, we disprove the conjecture, asserting that…