Zobrazeno 1 - 10
of 61
pro vyhledávání: '"Vlaar, Bart"'
Autor:
Appel, Andrea, Vlaar, Bart
We introduce a universal framework for boundary transfer matrices, inspired by Sklyanin's two-row transfer matrix approach for quantum integrable systems with boundary conditions. The main examples arise from quantum symmetric pairs of finite and aff
Externí odkaz:
http://arxiv.org/abs/2410.21654
Autor:
Appel, Andrea, Vlaar, Bart
Let $\mathfrak{g}$ be a symmetrizable Kac-Moody algebra, $U_q(\mathfrak{g})$ its quantum group, and $U_q(\mathfrak{k}) \subset U_q(\mathfrak{g})$ a quantum symmetric pair subalgebra determined by a Lie algebra automorphism $\theta$. We introduce a ca
Externí odkaz:
http://arxiv.org/abs/2402.16676
Publikováno v:
Approved for publication in Communications in Mathematical Physics (2024)
One of the features of Baxter's Q-operators for many closed spin chain models is that all transfer matrices arise as products of two Q-operators with shifts in the spectral parameter. In the representation-theoretical approach to Q-operators, underly
Externí odkaz:
http://arxiv.org/abs/2301.03997
Autor:
Appel, Andrea, Vlaar, Bart
Let $\mathfrak{g}$ be a complex simple Lie algebra and $U_q\hat{\mathfrak{g}}$ the corresponding quantum affine algebra. We prove that every irreducible finite-dimensional $U_q\hat{\mathfrak{g}}$-module gives rise to a family of trigonometric K-matri
Externí odkaz:
http://arxiv.org/abs/2203.16503
Publikováno v:
Lett. Math. Phys. 112, 78 (2022)
We examine classes of quantum algebras emerging from involutive, non-degenerate set-theoretic solutions of the Yang-Baxter equation and their q-analogues. After providing some universal results on quasi-bialgebras and admissible Drinfeld twists we sh
Externí odkaz:
http://arxiv.org/abs/2203.03400
Autor:
Regelskis, Vidas, Vlaar, Bart
Publikováno v:
in Hypergeometry, integrability and Lie theory, 155-203, Contemp. Math., 780, Amer. Math. Soc. (2022)
Lie algebra involutions and their fixed-point subalgebras give rise to symmetric spaces and real forms of complex Lie algebras, and are well-studied in the context of symmetrizable Kac-Moody algebras. In this paper we study a generalization. Namely,
Externí odkaz:
http://arxiv.org/abs/2108.00260
Autor:
Appel, Andrea, Vlaar, Bart
Publikováno v:
Represent. Theory 26 (2022), 764-824
We introduce the notion of a cylindrical bialgebra, which is a quasitriangular bialgebra $H$ endowed with a universal K-matrix, i.e., a universal solution of a generalized reflection equation, yielding an action of cylindrical braid groups on tensor
Externí odkaz:
http://arxiv.org/abs/2007.09218
Autor:
Vlaar, Bart, Weston, Robert
Publikováno v:
J. Phys. A: Math. Theor. 53 (2020) 245205
We construct a Q-operator for the open XXZ Heisenberg quantum spin chain with diagonal boundary conditions and give a rigorous derivation of Baxter's TQ relation. Key roles in the theory are played by a particular infinite-dimensional solution of the
Externí odkaz:
http://arxiv.org/abs/2001.10760
Autor:
Regelskis, Vidas, Vlaar, Bart
Let $\mathfrak{g}$ be a finite-dimensional semisimple complex Lie algebra and $\theta$ an involutive automorphism of $\mathfrak{g}$. According to G. Letzter, S. Kolb and M. Balagovi\'c the fixed-point subalgebra $\mathfrak{k} = \mathfrak{g}^\theta$ h
Externí odkaz:
http://arxiv.org/abs/1807.02388
Autor:
Regelskis, Vidas, Vlaar, Bart
We find the complete set of invertible solutions of the untwisted and twisted reflection equations for the Bazhanov-Jimbo R-matrix of type ${\mathrm A}^{(1)}_{N-1}$. We also show that all invertible solutions can be obtained by an appropriate affiniz
Externí odkaz:
http://arxiv.org/abs/1803.06491