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Related papers: Baxter Q-operator from quantum K-theory

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We propose a fibre bundle formulation of the mathematical base of relativistic quantum mechanics. At the present stage the bundle form of the theory is equivalent to its conventional one, but it admits new types of generalizations in…

Quantum Physics · Physics 2007-05-23 Bozhidar Z. Iliev

We study the fixed points of the universal G-equivariant n-dimensional complex vector bundle and obtain a decomposition formula in terms of twisted equivariant universal complex vector bundles of smaller dimension. We use this decomposition…

Algebraic Topology · Mathematics 2018-12-19 Andrés Angel , José Manuel Gómez , Bernardo Uribe

We consider the open spin-s XXZ quantum spin chain with nondiagonal boundary terms. By exploiting certain functional relations at roots of unity, we derive a generalized form of T-Q relation involving more than one independent Q(u), which…

Mathematical Physics · Physics 2015-06-05 Rashad Baiyasi , Rajan Murgan

In [1], the spectrum (eigenvalues and eigenstates) of a lattice regularizations of the Sine-Gordon model has been completely characterized in terms of polynomial solutions with certain properties of the Baxter equation. This…

High Energy Physics - Theory · Physics 2010-05-12 G. Niccoli

We show that the stochastic dynamics of a large class of one-dimensional interacting particle systems may be presented by integrable quantum spin Hamiltonians. Using the Bethe ansatz and similarity transformations this yields new exact…

Condensed Matter · Physics 2007-05-23 Gunter M. Schütz

We reexamine the massless spectrum of a heterotic string vacuum at large radius and present two results. The first result is to construct a vector bundle $\mathcal{Q}$ and operator $\overline{\mathcal{D}}$ whose kernel amounts to…

High Energy Physics - Theory · Physics 2022-11-30 Jock McOrist , Eirik Eik Svanes

We determine the ring structure of the equivariant quantum cohomology of the Hilbert scheme of points in the complex plane. The operator of quantum multiplication by the divisor class is a nonstationary deformation of the quantum…

Algebraic Geometry · Mathematics 2008-04-15 A. Okounkov , R. Pandharipande

We study the geometry and topology of (filtered) algebra-bundles ${\bf\Psi}^{\mathbb Z}$ over a smooth manifold $X$ with typical fibre $\Psi^{\mathbb Z}(Z; V)$, the algebra of classical pseudodifferential operators of integral order on the…

Differential Geometry · Mathematics 2017-10-18 Varghese Mathai , R. B. Melrose

Unitary braiding operators can be used as robust entangling quantum gates. We introduce a solution-generating technique to solve the $(d,m,l)$-generalized Yang-Baxter equation, for $m/2\leq l \leq m$, which allows to systematically…

Quantum Physics · Physics 2020-09-01 Pramod Padmanabhan , Fumihiko Sugino , Diego Trancanelli

The nested off-diagonal Bethe ansatz is generalized to study the quantum spin chain associated with the $SU_q(3)$ R-matrix and generic integrable non-diagonal boundary conditions. By using the fusion technique, certain closed operator…

Mathematical Physics · Physics 2016-08-24 Guang-Liang Li , Junpeng Cao , Kun Hao , Fakai Wen , Wen-Li Yang , Kangjie Shi

Yang-Baxter operators (YBOs) have been employed to construct quantum knot invariants. More recently, cohomology theories for YBOs have been independently developed, drawing inspiration from analogous theories for quandles and other discrete…

Geometric Topology · Mathematics 2025-11-17 Masahico Saito , Emanuele Zappala

We solve the longstanding problem to define a functional characterization of the spectrum of the transfer matrix associated to the most general spin-1/2 representations of the 6-vertex reflection algebra for general inhomogeneous chains.…

Mathematical Physics · Physics 2017-03-17 N. Kitanine , J. -M. Maillet , G. Niccoli

We define and study coherent states, a Berezin-Toeplitz quantization and covariant symbols on the product between a connected simply connected nilpotent Lie group and the dual of its Lie algebra. The starting point is a Weyl system…

Functional Analysis · Mathematics 2019-05-09 M. Mantoiu

The space of states and operators for a large class of background independent theories of quantum spacetime dynamics is defined. The SU(2) spin networks of quantum general relativity are replaced by labelled compact two-dimensional…

General Relativity and Quantum Cosmology · Physics 2016-08-25 Fotini Markopoulou , Lee Smolin

We describe the equivariant K-groups of a family of generalized Steinberg varieties that interpolates between the Steinberg variety of a reductive, complex algebraic group and its nilpotent cone in terms of the extended affine Hecke algebra…

Representation Theory · Mathematics 2013-11-26 J. Matthew Douglass , Gerhard Roehrle

We study the Yang-Baxter operator for the vector representation $V_m$ of the quantum group $U_q(sl_m)$. We consider the one-term Yang-Baxter homology with coefficients in $V_m$-modules and provide a direct sum decomposition of the one term…

Quantum Algebra · Mathematics 2025-05-07 Yin Tian , Xiao Wang , Yuxin Zhang

Studied is the Baxter equation for the quantum discrete Boussinesq equation. We explicitly construct the Baxter $\mathcal{Q}$ operator from a generating function of the local integrals of motion of the affine Toda lattice field theory, and…

Exactly Solvable and Integrable Systems · Physics 2011-07-19 Kazuhiro Hikami

We prove that "unitary deformation K-theory" takes products of finitely generated groups to coproducts of algebra spectra over ku, the connective K-theory spectrum. Additionally, we give spectral sequences for computing the homotopy groups…

K-Theory and Homology · Mathematics 2007-05-23 Tyler Lawson

We develop basic constructions of the Baxter operator formalism for the Macdonald polynomials associated with root systems of type A. Precisely we construct a dual pair of mutually commuting Baxter operators such that the Macdonald…

Algebraic Geometry · Mathematics 2015-06-04 Anton Gerasimov , Dimitri Lebedev , Sergey Oblezin

Let $\Gamma$ be a torsion-free arithmetic group acting on its associated global symmetric space $X$. Assume that $X$ is of non-compact type and let $\Gamma$ act on the geodesic boundary $\partial X$ of $X$. Via general constructions in…

K-Theory and Homology · Mathematics 2017-09-19 Bram Mesland , Mehmet Haluk Sengun