Lie Theory and Its Applications in Physics Varna, Bulgaria, June 2023

This volume presents modern trends in the area of symmetries and their applications based on contributions to the workshop "Lie Theory and Its Applications in Physics" held in Sofia (Bulgaria) in June 2023.

Traditionally, Lie theory is a tool to build mathematical models for physical systems. Recently, the trend is towards geometrization of the mathematical description of physical systems and objects. A geometric approach to a system yields in general some notion of symmetry, which is very helpful in understanding its structure. Geometrization and symmetries are meant in their widest sense, i.e., representation theory, algebraic geometry, number theory, infinite-dimensional Lie algebras and groups, superalgebras and supergroups, groups and quantum groups, noncommutative geometry, symmetries of linear and nonlinear partial differential operators, special functions, and others. Furthermore, the necessary tools from functional analysis are included. This is a large interdisciplinary and interrelated field.

The topics covered in this volume from the workshop represent the most modern trends in the field: Representation Theory, Symmetries in String Theories, Symmetries in Gravity Theories, Supergravity, Conformal Field Theory, Integrable Systems, Polylogarithms, and Supersymmetry. They also include Supersymmetric Calogero-type models, Quantum Groups, Deformations, Quantum Computing and Deep Learning, Entanglement, Applications to Quantum Theory, and Exceptional Quantum Algebra for the standard model of particle physics

This book is suitable for a broad audience of mathematicians, mathematical physicists, and theoretical physicists, including researchers and graduate students interested in Lie Theory.

Plenary Talks, T. Kobayashi, Short Proof for Rankin–Cohen Brackets and Generating Operators.- I. Todorov, The 2022 Nobel Prize in Physics.- P. Aschieri, G. Landi, C. Pagani, Quantum Gauge Groups of Quantum Principal Bundles.- D. Broadhurst, Multivariate Elliptic Kites and Tetrahedral Tadpoles.- S. Catto, Hurwitz Algebras at the Core of Classi?cation of Possible Symmetries in Hadronic Physics.- E. Guendelman, Braneworlds in Dynamical Tension String Theories.- M. Henkel, Generalised Time-Translation-Invariance in Simple Ageing.- V. Avramov, R. C. Rashkov, T. Vetsov, Remarks on Operator Growth and Certain Integrable Structures.- Nedialka I. Stoilova and Joris Van der Jeugt, Matrix Structure of Classical Z2 × Z2 Graded Lie Algebras.- G. Patellis, W. Porod and G. Zoupanos, Split NMSSM from Dimensional Reduction of a 10D, N = 1, E8 Theory Over a Modi?ed Flag Manifold.- String Theories, Gravity, Cosmology, L. Anguelova and C. Lazaroiu, Consistency Condition for Slow-roll and Rapid-turn In?ation.- I. Dimitrijevic´, B. Dragovich, Z. Rakic and J. Stankovic, On a Nonlocal de Sitter Gravity.- Denitsa Staicova, Cosmology in LIV Constraints from GRB Time-Delays.- H. Kunitomo, Superstring Field Theory with Homotopy Lie Algebra Structure.- V. Avramov, M. Radomirov, R.C. Rashkov and T. Vetsov, Classical Thermodynamic Stability of Reissner-Nordstrom-AdS Black  Hole.- Supersymmetry, E. Poletaeva, On Dual Modules over the Super-Yangian of Q(1).- N. Aizawa, Towards a Super?eld Formulation of Z22-Supersymmetry.- A. Nedelin, Elliptic Integrable Models and Their Spectra from Superconformal Indices.- N. Hage, A Super Littlewood–Richardson Type Rule.- Integrable Systems.- C. Burdik and O. Navratil, Dependence of Bethe Vectors for RTT–Type Algebra sp(4).- O. Vaneeva, O. Brahinets, O. Magda, A. Zhalij, Equivalence Groupoid and Exact Solutions of a Class of Generalized Modi?ed Korteweg–de Vries Equations.- N. Manojlovic and I. Salom, Bethe states for the periodic inhomogeneous SO(3) spin chain.- R. Abedin and S. Maximov, Twisted Standard Lie Bialgebra Structures on Loop Algebras.- Y. Nasuda, Harmonic Oscillator with a Step and Its Wigner Function.- T. Prochazka, W -Algebras and Integrability.-  Representation Theory, K. Arashi, Coherent State Representations of the Holomorphic Automorphism Group of a Quasi-Symmetric Siegel Domain of Type III.- P. Spacek and C. Wang, Canonical Mirror Models for Maximal Orthogonal Grassmannians.- B. Westbury, Series of Representations.- R. Stekolshchik, Remarks on Decompositions of the Longest Element of the Weyl Group.- V. Losert, On Matrix Coef?cients of Representations of SL(2, R).- V. K. Dobrev, Quaternionic Discrete Series and Invariant Differential Operators over the Lie Algebra F40.- Various Mathematical Results, A. Dobrogowska, Lie Algebroid Structures on Cotangent Bundles Determined by Vector Fields.- Valdemar V. Tsanov, Partial Convex Hulls of Coadjoint Orbits and Degrees of Invariants.- R. Campoamor-Stursberg and M. Rausch de Traubenberg, Kac-Moody and Virasoro Algebras on the Two-Sphere and the Two-Torus.- F. Januszewski, Families of D-Modules and Integral Models of (g, K)-Modules.- A. Mayeux, Magnets and Attractors of Diagonalizable Group Schemes Actions.- V. C. Bui, V. Hoang Ngoc Minh, Q.H. Ngo and V. Nguyen Dinh, On the Kernels of the Polymorphism Zeta.- C. Anghel and D. Cheptea, Ribbon Structures Derived from Homotopy Leibniz Algebras and Symplectic Lie Pairs.- Conformal Theories, T. Kojima, Quadratic Relations of the Deformed W -Algebra.- S. Stoimenov and M. Henkel, Meta-Schrodinger and Meta-Conformal Symmetries in the Non-Equilibrium Dynamics of the Directed Spherical Model.- D. Klyuev, A Different Approach to Positive Traces on Generalized q-Weyl Algebras.- Gizem S¸eng, Searching for Discrete Series Representations at the Late-Time Boundary of de Sitter, H. Pejhan, de Sitter Relativity Group.- Applications of Holography, Ph. Nounahon and Todor Popov, Landau Levels for the Haldane’s Spheres.- V. Avramov, H. Dimov, M. Radomirov, R.C. Rashkov, T. Vetsov, Thermodynamic Length and Optimal Processes in Holographic Models.- Chen-Te Ma, Modular Average and Weyl Anomaly in Two-Dimensional Schwarzian Theory.- Applications to Quantum Theory, A. Sako, Lie Algebra and Quantization in Quantum World.- Otto C.W. Kong, Lorentz Covariant Quantum Particle Dynamics from the Proper Symmetry Theoretical Formulation.- E. I. Jafarov, S. M. Nagiyev, J. Van der Jeugt, The Semicon?ned Harmonic Oscillator with a Position-Dependent Effective Mass: Exact Solution, Dynamical Symmetry Algebra and Quasiprobability Distribution Functions.