Zobrazeno 1 - 10
of 47
pro vyhledávání: '"Gorbounov, Vassily"'
In this paper we relate a well-known in symplectic geometry compactification of the space of symmetric bilinear forms on the Lagrangian Grassmannian to the specific compactifications of the space of electrical networks in the disc obtained in \cite{L
Externí odkaz:
http://arxiv.org/abs/2406.03021
We generalize the electrical Lie algebras originally introduced by Lam and Pylyavskyy in several ways. To each Kac-Moody Lie algebra $\mathfrak{g}$ we associate two types (vertex type and edge type) of the generalized electrical algebras. The electri
Externí odkaz:
http://arxiv.org/abs/2405.02956
We refine the result of T. Lam \cite{L} on embedding the space $E_n$ of electrical networks on a planar graph with $n$ boundary points into the totally non-negative Grassmannian $\mathrm{Gr}_{\geq 0}(n-1,2n)$ by proving first that the image lands in
Externí odkaz:
http://arxiv.org/abs/2109.13952
Autor:
Gorbounov, Vassily, Schechtman, Vadim
Publikováno v:
SIGMA 17 (2021), 001, 26 pages
In the work of Mukhin and Varchenko from 2002 there was introduced a Wronskian map from the variety of full flags in a finite dimensional vector space into a product of projective spaces. We establish a precise relationship between this map and the P
Externí odkaz:
http://arxiv.org/abs/2007.04045
Autor:
Gorbounov, Vassily, Talalaev, Dmitry
We propose a new approach to studying electrical networks interpreting the Ohm law as the operator which solves certain Local Yang-Baxter equation. Using this operator and the medial graph of the electrical network we define a vertex integrable stati
Externí odkaz:
http://arxiv.org/abs/1905.03522
We present a simple but explicit example of a recent development which connects quantum integrable models with Schubert calculus: there is a purely geometric construction of solutions to the Yang-Baxter equation and their associated Yang-Baxter algeb
Externí odkaz:
http://arxiv.org/abs/1802.09497
We show that the local observables of the curved beta gamma system encode the sheaf of chiral differential operators using the machinery of the book "Factorization algebras in quantum field theory", by Kevin Costello and the second author, which comb
Externí odkaz:
http://arxiv.org/abs/1610.09657
In his extension of W. Siegel's ideas on string quantization, N. Berkovits made several observations which deserve further study and development. Indeed, interesting accounts of this work have already appeared in the mathematical literature and in a
Externí odkaz:
http://arxiv.org/abs/1504.07489
Autor:
Gorbounov, Vassily, Korff, Christian
Publikováno v:
Advances in Mathematics, Volume 313, 20 June 2017, Pages 282-356
We introduce and study a new mathematical structure in the generalised (quantum) cohomology theory for Grassmannians. Namely, we relate the Schubert calculus to a quantum integrable system known in the physics literature as the asymmetric six-vertex
Externí odkaz:
http://arxiv.org/abs/1408.4718
Autor:
Gorbounov, Vassily, Korff, Christian
There are two intriguing statements regarding the quantum cohomology of partial flag varieties. The first one relates quantum cohomology to the affinisation of Lie algebras and the homology of the affine Grassmannian, the second one connects it with
Externí odkaz:
http://arxiv.org/abs/1402.2907