Pieri rules for the Jack polynomials in superspace and the 6-vertex model

Gatica, Jessica; Jones, Miles; Lapointe, Luc

doi:10.48550/arxiv.1712.02416

Cited by 2 publications

(4 citation statements)

References 6 publications

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“…Pieri rules. Pieri rules for the Macdonald polynomials in superspace that generalize those of the Jack polynomials in superspace (see Section 3.5.6) were conjectured in [17].…”

Section: Conjecture 43 -(Positivitymentioning

confidence: 99%

“…A generalization of symmetric function theory to superspace has been developed over the last 15 years (see for instance [11][12][13][14][15][16][17]). Such a generalization involves the anticommuting variables θ 1 , .…”

Section: Introductionmentioning

confidence: 99%

“…Explicit formulas for the coefficients, d ΛΩ (α) and dΛΩ (α) are provided in [17]. Remarkably, the non-linear factor described previously turns out to be a determinant related to the partition function of the 6-vertex model in statistical mechanics while the remaining linear factors can be expressed, as in the usual Jack polynomial case, in terms of certain hook-lengths in a Ferrers' diagram.…”

mentioning

confidence: 95%

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Symmetric functions in superspace: a compendium of results and open problems (including a SageMath worksheet)

Alarie-Vézina¹,

Blondeau-Fournier²,

Desrosiers³

et al. 2019

Preprint

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We present a review of the most important results in the theory of symmetric functions in superspace (or symmetric superpolynomials), summarizing all principal contributions since its introduction in 2001 in the context of the supersymmetric Calogero-Moser-Sutherland integrable model. We also mention some open problems which remain unanswered at this moment, in particular the connection with representation theory. In addition, we provide a free open access source code, relying on SageMath library, that can be used as a research tool for symmetric superpolynomials. The content is directed to an audience new to this research area, but who is familiar with the classical theory of symmetric functions.

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“…Pieri rules. Pieri rules for the Macdonald polynomials in superspace that generalize those of the Jack polynomials in superspace (see Section 3.5.6) were conjectured in [17].…”

Section: Conjecture 43 -(Positivitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 95%

See 1 more Smart Citation

Symmetric functions in superspace: a compendium of results and open problems (including a SageMath worksheet)

Alarie-Vézina¹,

Blondeau-Fournier²,

Desrosiers³

et al. 2019

Preprint

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show abstract

“…Most of the important features of the Macdonald polynomials seem to extend to superspace. The duality and the existence of Macdonald operators were shown for instance in [5] while various properties were conjectured to hold such as explicit formulas for the norm and the evaluation [4], Pieri rules (which connect to the 6-vertex model) [9] and symmetry [3]. Most remarkably, an extension of the original Macdonald positivity conjecture was stated in [5].…”

Section: Introductionmentioning

confidence: 99%