Zobrazeno 1 - 10
of 73
pro vyhledávání: '"Garbali, A."'
Starting from the Izergin-Korepin 19-vertex model in the quadrant, we introduce two families of rational multivariate functions $F_S$ and $G_S$; these are in direct analogy with functions introduced by Borodin in the context of the higher-spin 6-vert
Externí odkaz:
http://arxiv.org/abs/2412.18085
We study the stochastic six-vertex model in half-space with generic integrable boundary weights, and define two families of multivariate rational symmetric functions. Using commutation relations between double-row operators, we prove a skew Cauchy id
Externí odkaz:
http://arxiv.org/abs/2312.14348
Autor:
Garbali, Alexandr, Gunna, Ajeeth
We consider partition functions on the $N\times N$ square lattice with the local Boltzmann weights given by the $R$-matrix of the $U_{t}(\widehat{sl}(n+1|m))$ quantum algebra. We identify boundary states such that the square lattice can be viewed on
Externí odkaz:
http://arxiv.org/abs/2312.06138
A $(q,t)$-deformation of the 2d Toda integrable hierarchy is introduced by enhancing the underlying symmetry algebra $\mathfrak{gl}(\infty)\simeq \text{q-W}_{1+\infty}$ to the quantum toroidal $\mathfrak{gl}(1)$ algebra. The difference-differential e
Externí odkaz:
http://arxiv.org/abs/2308.16583
Autor:
Garbali, Alexandr, Gunna, Ajeeth ⁎
Publikováno v:
In Advances in Mathematics December 2024 458 Part B
Autor:
Garbali, Alexandr, Neguţ, Andrei
We consider the problem of the R-matrix of the quantum toroidal algebra $U_{q,t}(\ddot{\mathfrak{gl}}_1)$ in the Fock representation. Using the connection between the R-matrix $R(u)$ ($u$ being the spectral parameter) and the theory of Macdonald oper
Externí odkaz:
http://arxiv.org/abs/2112.09094
Autor:
Garbali, Alexandr, Zinn-Justin, Paul
The commutative trigonometric shuffle algebra ${\mathrm A}$ is a space of symmetric rational functions satisfying certain wheel conditions. We describe a ring isomorphism between ${\mathrm A}$ and the center of the Hecke algebra using a realization o
Externí odkaz:
http://arxiv.org/abs/2110.07155
Autor:
Garbali, Alexandr, de Gier, Jan
Publikováno v:
Commun. Math. Phys. 384 (2021), 1971-2008
We propose a method to compute the $R$-matrix $R$ on a tensor product of Fock modules from coproduct relations in a Hopf algebra. We apply this method to the quantum toroidal algebra $U_{q,t}(\overset{..}{gl}_1)$ for which $R$ is currently not explic
Externí odkaz:
http://arxiv.org/abs/2004.09241
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