Proving superintegrability in $\beta$-deformed eigenvalue models

Bawane, Aditya; Karimi, Pedram; Sułkowski, Piotr

doi:10.21468/scipostphys.13.3.069

Cited by 7 publications

(4 citation statements)

References 19 publications

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“…The other generalization is the so-called β-deformation. It has already been noticed in [3][4][5][6], that W -operators can be β-deformed. The main ingredient is the deformed operator W 0 , which is nothing but the Calogero-Sutherland hamiltonian:…”

Section: Introductionmentioning

confidence: 94%

“…Particular reduction of these expansions involves several cases well known in the literature such as: 27), it gives the supposed β-deformed of the complex (square) matrix model with a logarithmic insertion of [6,14]:…”

Section: Partition Functions In Terms Of ŵ(N)mentioning

confidence: 99%

“…) in ( 27), it gives the β-deformed eigenvalue whose potential is the Gaussian potential with a linear term [6,14]:…”

Section: Partition Functions In Terms Of ŵ(N)mentioning

confidence: 99%

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$W$-representations for multi-character partition functions and their $β$-deformations

Wang¹,

V.²,

A.³

et al. 2023

Preprint

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In this letter we continue the development of W -representations. We propose several generalizations of the known models, such as the hypergeometric Hurwitz τ -functions. We construct W -representations for multi-character expansions, which involve a generic number of sets of time variables. We propose integral representations for such kind of partition functions which are given by tensor models and multi-matrix models with multi-trace couplings. We further propose the β-deformation of the discussed W -representation for the Hurwitz case for two sets of times as well as for the multi-character case.

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Section: Introductionmentioning

confidence: 94%

Section: Partition Functions In Terms Of ŵ(N)mentioning

confidence: 99%

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$W$-representations for multi-character partition functions and their $β$-deformations

Wang¹,

V.²,

A.³

et al. 2023

Preprint

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“…• S R provide the superintegrable basis [32][33][34][35][36][37][38][39][40][41][42] in matrix models.…”

Section: Motivationmentioning

confidence: 99%

3-Schurs from explicit representation of Yangian $$ \textrm{Y}\left({\hat{\mathfrak{gl}}}_1\right) $$. Levels 1–5

Morozov,

Tselousov

2023

J. High Energ. Phys.

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We suggest an ansatz for representation of affine Yangian $$ Y\left({\hat{\mathfrak{gl}}}_1\right) $$ Y gl ̂ 1 by differential operators in the triangular set of time-variables Pa,i with 1 ⩽ i ⩽ a, which saturates the MacMahon formula for the number of 3d Young diagrams/plane partitions. In this approach the 3-Schur polynomials are defined as the common eigenfunctions of an infinite set of commuting “cut-and-join” generators ψn of the Yangian. We manage to push this tedious program through to the 3-Schur polynomials of level 5, and this provides a rather big sample set, which can be now investigated by other methods.

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