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AIP Conference Proceedings, 1993 These notes correspond rather accurately to the translation of the lectures given at the Fifth Mexican School of Particles and Fields, held in Guanajuato, Gto., in December~1992.
Ruiz--Altaba, M.
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QUANTUM DISSIPATION AND QUANTUM GROUPS [PDF]
Annals of Physics, 1995 We discuss the r\^ole of quantum deformation of Weyl-Heisenberg algebra in dissipative systems and finite temperature systems. We express the time evolution generator of the damped harmonic oscillator and the generator of thermal Bogolubov ...
Iorio, Alfredo, Vitiello, Giuseppe
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Fixed Point Algebras for Easy Quantum Groups [PDF]
, 2016 Compact matrix quantum groups act naturally on Cuntz algebras. The first author isolated certain conditions under which the fixed point algebras under this action are Kirchberg algebras. Hence they are completely determined by their $K$-groups.
Gabriel, Olivier, Weber, Moritz
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A note on quantum subgroups of free quantum groups
Comptes Rendus. MathématiqueIn this short note, quantum subgroups in finite free products of the Pontryagin duals of free unitary quantum groups are classified. They correspond to pairs of a subgroup $\Gamma $ and a subset $S$ of the free group $\mathbb{F}_n$ such that $S$ is ...
Hoshino, Mao, Kitamura, Kan
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Solutions by Quadratures of Complex Bernoulli Differential Equations and Their Quantum Deformation
Axioms, 2023 It is shown that the complex Bernoulli differential equations admitting the supplementary structure of a Lie–Hamilton system related to the book algebra b2 can always be solved by quadratures, providing an explicit solution of the equations. In addition,
Rutwig Campoamor-Stursberg +2 more
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A representation-theoretic proof of the branching rule for Macdonald polynomials [PDF]
Discrete Mathematics & Theoretical Computer Science, 2015 We give a new representation-theoretic proof of the branching rule for Macdonald polynomials using the Etingof-Kirillov Jr. expression for Macdonald polynomials as traces of intertwiners of $U_q(gl_n)$. In the Gelfand-Tsetlin basis, we show that diagonal
Yi Sun
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Quantum groups and polymer quantum mechanics [PDF]
Modern Physics Letters A, 2021 In Polymer Quantum Mechanics, a quantization scheme that naturally emerges from Loop Quantum Gravity, position and momentum operators cannot be both well defined on the Hilbert space [Formula: see text]. It is henceforth deemed impossible to define standard creation and annihilation operators.
Acquaviva G., Iorio A., Smaldone L.
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UNIVERSAL QUANTUM GROUPS [PDF]
International Journal of Mathematics, 1996 For each invertible m×m matrix Q a compact matrix quantum group Au(Q) is constructed. These quantum groups are shown to be universal in the sense that any compact matrix quantum group is a quantum subgroup of some of them. Their orthogonal version Ao(Q) is also constructed. Finally, we discuss related constructions in the literature.
Van Daele, Alfons, Wang, Shuzhou
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Quantum Channels with Quantum Group Symmetry [PDF]
Communications in Mathematical Physics, 2022 In this paper we will demonstrate that any compact quantum group can be used as symmetry groups for quantum channels, which leads us to the concept of covariant channels. We, then, unearth the structure of the convex set of covariant channels by identifying all extreme points under the assumption of multiplicity-free condition for the associated fusion
Hun Hee Lee, Sang-Gyun Youn
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Quantum groups and quantum cohomology [PDF]
Astérisque, 2019 In this paper, we study the classical and quantum equivariant cohomology of Nakajima quiver varieties for a general quiver Q. Using a geometric R-matrix formalism, we construct a Hopf algebra Y_Q, the Yangian of Q, acting on the cohomology of these varieties, and show several results about their basic structure theory.
Maulik, D, Okounkov, A
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