Zobrazeno 1 - 10
of 89
pro vyhledávání: '"Gainutdinov, Azat M."'
We consider the link and three-manifold invariants in [DGGPR], which are defined in terms of certain non-semisimple finite ribbon categories $\mathcal{C}$ together with a choice of tensor ideal and modified trace. If the ideal is all of $\mathcal{C}$
Externí odkaz:
http://arxiv.org/abs/2307.06069
We study universal solutions to reflection equations with a spectral parameter, so-called K-operators, within a general framework of universal K-matrices - an extended version of the approach introduced by Appel-Vlaar. Here, the input data is a quasi
Externí odkaz:
http://arxiv.org/abs/2301.00781
Publikováno v:
SIGMA 19 (2023), 046, 47 pages
We derive by the traditional algebraic Bethe ansatz method the Bethe equations for the general open XXZ spin chain with non-diagonal boundary terms under the Nepomechie constraint [J. Phys. A 37 (2004), 433-440, arXiv:hep-th/0304092]. The technical d
Externí odkaz:
http://arxiv.org/abs/2212.09696
Publikováno v:
J. of High Energy Phys. 2022 16 (2022)
We introduce new $U_q\mathfrak{sl}_2$-invariant boundary conditions for the open XXZ spin chain. For generic values of $q$ we couple the bulk Hamiltonian to an infinite-dimensional Verma module on one or both boundaries of the spin chain, and for $q=
Externí odkaz:
http://arxiv.org/abs/2207.12772
Publikováno v:
Selecta Math. New Ser. 30, article number 26 (2024)
Davydov--Yetter (DY) cohomology classifies infinitesimal deformations of the monoidal structure of tensor functors and tensor categories. In this paper we provide new tools for the computation of the DY cohomology for finite tensor categories and exa
Externí odkaz:
http://arxiv.org/abs/2202.12287
Publikováno v:
Nucl. Phys. B 979 (2022) 115789
We continue investigating the generalisations of geometrical statistical models introduced in [13], in the form of models of webs on the hexagonal lattice H having a U_q(sl_n) quantum group symmetry. We focus here on the n=3 case of cubic webs, based
Externí odkaz:
http://arxiv.org/abs/2107.10106
Publikováno v:
In Nuclear Physics, Section B May 2024 1002
Publikováno v:
J. Stat. Mech. (2021) 053104
This is the first in a series of papers devoted to generalisations of statistical loop models. We define a lattice model of $U_q(\mathfrak{sl}_n)$ webs on the honeycomb lattice, for $n \ge 2$. It is a statistical model of closed, cubic graphs with ce
Externí odkaz:
http://arxiv.org/abs/2101.00282
Publikováno v:
Commun. Contemp. Math. (2021), 2150091
In [arXiv:1912.02063], we constructed 3-dimensional Topological Quantum Field Theories (TQFTs) using not necessarily semisimple modular categories. Here, we study projective representations of mapping class groups of surfaces defined by these TQFTs,
Externí odkaz:
http://arxiv.org/abs/2010.14852
Publikováno v:
J. of Pure and Applied Algebra, 225 (2021) 106678
For $\mathcal{C}$ a finite tensor category we consider four versions of the central monad, $A_1, \dots, A_4$ on $\mathcal{C}$. Two of them are Hopf monads, and for $\mathcal{C}$ pivotal, so are the remaining two. In that case all $A_i$ are isomorphic
Externí odkaz:
http://arxiv.org/abs/2003.13307