Inverse spectral problem for Jacobi operators and Miura transformation
Concrete Operators, 2021 We study a Miura-type transformation between Kac - van Moerbeke (Volterra) and Toda lattices in terms of the inverse spectral problem for Jacobi operators, which appear in the Lax representation for such systems.
Osipov Andrey
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Partial categorification of Hopf algebras and representation theory of towers of \mathcalJ-trivial monoids [PDF]
Discrete Mathematics & Theoretical Computer Science, 2014 This paper considers the representation theory of towers of algebras of $\mathcal{J} -trivial$ monoids. Using a very general lemma on induction, we derive a combinatorial description of the algebra and coalgebra structure on the Grothendieck rings $G_0 ...
Aladin Virmaux
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Geometric algebra and algebraic geometry of loop and Potts models
Journal of High Energy Physics, 2022 We uncover a connection between two seemingly separate subjects in integrable models: the representation theory of the affine Temperley-Lieb algebra, and the algebraic structure of solutions to the Bethe equations of the XXZ spin chain.
Janko Böhm +3 more
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Searching for continuous phase transitions in 5D SU(2) lattice gauge theory
Journal of High Energy Physics, 2021 We study the phase diagram of 5-dimensional SU(2) Yang-Mills theory on the lattice. We consider two extensions of the fundamental plaquette Wilson action in the search for the continuous phase transition suggested by the 4 + ϵ expansion.
Adrien Florio +3 more
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Big Data Mining: a Computer-Oriented Method of Working with the Semantics of Assertions
Современные информационные технологии и IT-образование, 2021 When analyzing large amounts of data with the involvement of experts of subject domain, the problem of knowledge representation arises, this problem lies in describing the semantic content of judgments with their subsequent formalization, automated ...
Galina Goremykina
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SERRE WEIGHTS AND BREUIL’S LATTICE CONJECTURE IN DIMENSION THREE
Forum of Mathematics, Pi, 2020 We prove in generic situations that the lattice in a tame type induced by the completed cohomology of a $U(3)$-arithmetic manifold is purely local, that is, only depends on the Galois representation at places above $p$. This is a generalization to $\text{
DANIEL LE +3 more
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Graphical Models in Reconstructability Analysis and Bayesian Networks
Entropy, 2021 Reconstructability Analysis (RA) and Bayesian Networks (BN) are both probabilistic graphical modeling methodologies used in machine learning and artificial intelligence.
Marcus Harris, Martin Zwick
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Thermodynamics of three-dimensional Kitaev quantum spin liquids via tensor networks
Physical Review Research, 2021 We study the 3D Kitaev and Kitaev-Heisenberg models, respectively, on the hyperhoneycomb and hyperoctagon lattices, both at zero and finite-temperature, in the thermodynamic limit.
Saeed S. Jahromi +2 more
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Speeding Up Learning Quantum States Through Group Equivariant Convolutional Quantum Ansätze
PRX Quantum, 2023 We develop a theoretical framework for S_{n}-equivariant convolutional quantum circuits with SU(d) symmetry, building on and significantly generalizing Jordan’s permutational quantum computing formalism based on Schur-Weyl duality connecting both SU(d ...
Han Zheng +4 more
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Variable-basis Categorically-algebraic Dualities
Fuzzy Information and Engineering, 2014 The manuscript continues our study on developing a categorically-algebraic (catalg) analogue of the theory of natural dualities of D. Clark and B. Davey, which provides a machinery for obtaining topological representations of algebraic structures.
Sergey A. Solovyov
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