Multiparameter Schur Q-Functions Are Solutions of the BKP Hierarchy

Rozhkovskaya, Natasha

doi:10.3842/sigma.2019.065

Cited by 10 publications

(15 citation statements)

References 15 publications

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“…Let {ϕ i } i∈Z be coefficients of the expansion ϕ(u) = j∈Z ϕ j u −j . Similarly to Proposition 3.1 one proves the following statements [13].…”

Section: Neutral Fermions Action On the Boson Fock Space Through All ...supporting

confidence: 64%

“…By Remark 4.1, τ = 1 is a tau-function of the BKP hierarchy. Similarly to Lemma 3.2 and statements of [13] we prove the following lemma.…”

Section: 2mentioning

confidence: 64%

“…]. From (2.6) it is clear that B odd is invariant with respect to action of e ⊥ k , and h ⊥ k , and one can prove [13] that restrictions to B odd of the operators E ⊥ (u), H ⊥ (u), S ⊥ (u) coincide. We can define the following formal distribution of operators acting on B odd :…”

Section: Neutral Fermions Action On the Boson Fock Space Through All ...mentioning

confidence: 99%

“…In particular, they showed in [8], [10] that any polynomial tau-function of the KP-hierarchy is obtained from a Schur polynomial by certain shifts of arguments, and in [9] they proved that any polynomial tau-function of the BKP or the DKP hierarchy is described by a Pfaffian formula that can be also related to Schur Q-polynomials by certain shifts of arguments. In the recent paper [13] the second author showed that the modes of certain generating series, involving Schur Q-polynomials, are tau-functions of the BKP hierarchy.…”

Section: Introductionmentioning

confidence: 99%

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Polynomial tau-functions of the KP, BKP, and the s-component KP hierarchies

Kač

Rozhkovskaya

Leur

2021

Journal of Mathematical Physics

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We show that any polynomial tau-function of the s-component KP and the BKP hierarchies can be interpreted as a zero mode of an appropriate combinatorial generating function.As an application, we obtain explicit formulas for all polynomial tau-functions of these hierarchies in terms of Schur polynomials and Q-Schur polynomials respectively. We also obtain formulas for polynomial tau-functions of the reductions of the s-component KP hierarchy associated to partitions in s parts.

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“…Let {ϕ i } i∈Z be coefficients of the expansion ϕ(u) = j∈Z ϕ j u −j . Similarly to Proposition 3.1 one proves the following statements [13].…”

Section: Neutral Fermions Action On the Boson Fock Space Through All ...supporting

confidence: 64%

“…By Remark 4.1, τ = 1 is a tau-function of the BKP hierarchy. Similarly to Lemma 3.2 and statements of [13] we prove the following lemma.…”

Section: 2mentioning

confidence: 64%

Section: Neutral Fermions Action On the Boson Fock Space Through All ...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Polynomial tau-functions of the KP, BKP, and the s-component KP hierarchies

Kač

Rozhkovskaya

Leur

2021

Journal of Mathematical Physics

Self Cite

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“…The initial motivation for this project was the study of tau-functions of the KP and the BKP hierarchy [6,7,8,9,19,49] by generalizing the methods of [47], where the author proved that the multiparameter Schur Q-functions are tau-functions of the BKP hierarchy. We aimed to provide a description of all polynomial tau-functions of the KP and the BKP hierarchies unifying the ideas of [47] and [27]. This is done in Section 6.…”

Section: Introductionmentioning

confidence: 99%

Linear transformations of vertex operator presentations of Hall-Littlewood polynomials

Rozhkovskaya¹

2022

Preprint

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We study the effect of linear transformations on quantum fields with applications to vertex operator presentations of symmetric functions. Properties of linearly transformed quantum fields and corresponding transformations of Hall-Littlewood polynomials are described, including preservation of commutation relations, stability, explicit combinatorial formulas and generating functions. We prove that specializations of linearly transformed Hall-Littlewood polynomials describe all polynomial tau functions of the KP and the BKP hierarchy. Examples of linear transformations are related to multiparameter symmetric functions, Grothendieck polynomials, deformations by cyclotomic polynomials, and some other variations of Schur symmetric functions that exist in the literature.

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Linear Transformations of Vertex Operators of Hall–Littlewood Polynomials

Rozhkovskaya

2023

J Math Sci

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We study the effect of linear transformations on quantum fields with applications to vertex operator presentations of symmetric functions. Properties of linearly transformed quantum fields and corresponding transformations of Hall-Littlewood polynomials are described, including preservation of commutation relations, stability, explicit combinatorial formulas, and generating functions. We prove that specializations of linearly transformed Hall-Littlewood polynomials describe all polynomial tau-functions of the KP and BKP hierarchies. Examples of linear transformations are related to multiparameter symmetric functions, Grothendieck polynomials, deformations by cyclotomic polynomials, and some other variations of Schur symmetric functions that exist in the literature. Bibliography: 57 titles.

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Multiparameter Schur Q-Functions Are Solutions of the BKP Hierarchy

Abstract: We prove that multiparameter Schur Q-functions, which include as specializations factorial Schur Q-functions and classical Schur Q-functions, provide solutions of BKP hierarchy.

Cited by 10 publications

References 15 publications

Polynomial tau-functions of the KP, BKP, and the s-component KP hierarchies

Polynomial tau-functions of the KP, BKP, and the s-component KP hierarchies

Linear transformations of vertex operator presentations of Hall-Littlewood polynomials

Linear Transformations of Vertex Operators of Hall–Littlewood Polynomials

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