Unified -deformation of oscillator algebra and two-dimensional conformal field theory

Burban, Igor

doi:10.1016/j.physleta.2013.08.044

Cited by 5 publications

(3 citation statements)

References 39 publications

(84 reference statements)

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“…The generalized (p, q; α, γ, l)-deformed Chakrabarti-Jagannathan version of the oscillator algebra. In [19],…”

Section: Oscillator Algebra and Its Unified Deformationsmentioning

confidence: 99%

“…In this article, we include the short review of our publication [19] on the construction of the unified (p, q; α, γ, l)-deformation of the oscillator algebras which envelop, as particular cases, the well-known deformations [1-3, 5, 17, 18]. The structure functions ("generalized (p, q; α, γ, l)-numbers") of these deformations [19] generalize the (p, q; α, γ, l)-deformation of the oscillator algebra:…”

Section: Introductionmentioning

confidence: 99%

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Unified (p, q; α, γ, l)-Deformations of Oscillator and Hybrid Oscillator Algebras and Two-Dimensional Conformal Field Theory

I.M.¹

2013

Ukr. J. Phys.

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The unified multiparametric generalizations of the well-known two-parameter deformed oscillator and hybrid oscillator algebras are introduced. The basic versions of these deformations are obtained by imputing the new free parameters in the structure functions and by a generalization of defining relations of these algebras. The generalized Jordan-Schwinger and Holstein-Primakoff realizations of the U αγl pq (su(2)) algebra by the creations and annihilations operators of the basic versions of these deformations are found. The (p, q; α, γ, l)-deformation of the two-dimensional conformal field theory is considered. The pole structure of the (p, q; α, γ, l)deformed operator product expansion (OPE) of the holomorphic component of the energymomentum tensor with primary fields is found. The two-point correlation function of the (p, q; α, γ, l)-deformed two-dimensional conformal field theory is calculated. K e y w o r d s: generalized deformed oscillator algebra, structure function, generalized Jordan-Schwinger and Holstein-Primakoff transformations, deformed two-dimensional conformal field theory.

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“…The generalized (p, q; α, γ, l)-deformed Chakrabarti-Jagannathan version of the oscillator algebra. In [19],…”

Section: Oscillator Algebra and Its Unified Deformationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Unified (p, q; α, γ, l)-Deformations of Oscillator and Hybrid Oscillator Algebras and Two-Dimensional Conformal Field Theory

I.M.¹

2013

Ukr. J. Phys.

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“…E is also conjectured in [31] to be isomorphic to the spherical double affine Hecke algebra (sDAHA) built in [36]. More importantly in the context of the six-dimensional origin of AGT correspondence [37,38], this algebra E is essentially equivalent to the Ding-Iohara-Miki (DIM) [33,39] algebra, also called quantum toroidal gl 1 [40,41] or elliptic Hall algebra [42]. 1 The covariance of the partition function under the algebra E originates a set of Ward identities between the correlators of the theory.…”

Section: Introductionmentioning

confidence: 99%

Coherent states in quantum $\mathcal{W}_{1+\infty}$ algebra and qq-character for 5d Super Yang-Mills

Bourgine,

Fukuda,

Matsuo

et al. 2016

Preprint

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The instanton partition functions of N = 1 5d super Yang-Mills are built using elements of the representation theory of quantum W 1+∞ algebra: Gaiotto state, intertwiner, vertex operator. This algebra is also known under the names of Ding-Iohara-Miki and quantum toroidal gl(1) algebra. Exploiting the explicit action of the algebra on the partition function, we prove the regularity of the 5d qq-characters. These characters provide a solution to the Schwinger-Dyson equations, and they can also be interpreted as a quantum version of the Seiberg-Witten curve.

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The algebra of two dimensional generalized Chebyshev-Koornwinder oscillator

Borzov

Damaskinsky²

2014

Journal of Mathematical Physics

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In the previous works of Borzov and Damaskinsky [“Chebyshev-Koornwinder oscillator,” Theor. Math. Phys. 175(3), 765–772 (2013)] and [“Ladder operators for Chebyshev-Koornwinder oscillator,” in Proceedings of the Days on Diffraction, 2013], the authors have defined the oscillator-like system that is associated with the two variable Chebyshev-Koornwinder polynomials. We call this system the generalized Chebyshev-Koornwinder oscillator. In this paper, we study the properties of infinite-dimensional Lie algebra that is analogous to the Heisenberg algebra for the Chebyshev-Koornwinder oscillator. We construct the exact irreducible representation of this algebra in a Hilbert space $\mathcal {H}$H of functions that are defined on a region which is bounded by the Steiner hypocycloid. The functions are square-integrable with respect to the orthogonality measure for the Chebyshev-Koornwinder polynomials and these polynomials form an orthonormalized basis in the space $\mathcal {H}$H. The generalized oscillator which is studied in the work can be considered as the simplest nontrivial example of multiboson quantum system that is composed of three interacting oscillators.

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Unified -deformation of oscillator algebra and two-dimensional conformal field theory

Cited by 5 publications

References 39 publications

Unified (p, q; α, γ, l)-Deformations of Oscillator and Hybrid Oscillator Algebras and Two-Dimensional Conformal Field Theory

Unified (p, q; α, γ, l)-Deformations of Oscillator and Hybrid Oscillator Algebras and Two-Dimensional Conformal Field Theory

Coherent states in quantum $\mathcal{W}_{1+\infty}$ algebra and qq-character for 5d Super Yang-Mills

The algebra of two dimensional generalized Chebyshev-Koornwinder oscillator

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