Representation Theory of Lattice Current Algebras [PDF]
Communications in Mathematical Physics, 1998 35 pages, LaTeX file, the revised version of the paper, to be published in Commun. Math. Phys.
Alekseev, Anton Y. +3 more
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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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Lattices of paths: Representation theory and valuations [PDF]
Journal of Combinatorics, 2011 We study some distributive lattices arising in the combinatorics of lattice paths. In particular, for the Dyck, Motzkin and Schroder lattices we describe the spectrum and we determine explicitly the Euler characteristic in terms of natural parameters of lattice paths.
FERRARI, LUCA, E. Munarini
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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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Path integral for the loop representation of lattice gauge theories [PDF]
Physical Review D, 1996 We show how the Hamiltonian lattice loop representation can be cast straightforwardly in the path integral formalism. The procedure is general for any gauge theory. Here we present in detail the simplest case: pure compact QED. We also analyze the non-Abelian Yang-Mills theory.
Aroca, J. M., Fort, H., Gambini, R.
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Band Theory and Boundary Modes of High-Dimensional Representations of Infinite Hyperbolic Lattices
Physical Review Letters, 2022 10 pages, 4 ...
Nan Cheng +5 more
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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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The Lagrangian loop representation of lattice U(1) gauge theory [PDF]
Physics Letters B, 1994 13 pp, UAB-FT-341 ...
Aroca, J. M., Baig, M., Fort, H.
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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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