Dual Multiparameter Schur Q-Functions

Korotkikh, Sergei

doi:10.1007/s10958-017-3412-6

Cited by 4 publications

(6 citation statements)

References 2 publications

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“…, u l ) up to a sign coincides with a classical Schur Q-function labeled by an appropriate strict partition. In [13] the following remarkable observation is made. The theorem is proved by induction on the length of the vector λ with the use of the fact that for any sequence a = (0, a 1 , a 2 , .…”

Section: Multiparameter Schur Q-functions Are Solutions Of Bkp Hierarchymentioning

confidence: 90%

“…where (−1) σ is the sign of permutation σ ( [13], Proposition 3). Hence, Q (a) α = 0 if α i = α j for some i, j, and for a vector α = (α 1 , .…”

Section: Multiparameter Schur Q-functions Are Solutions Of Bkp Hierarchymentioning

confidence: 99%

“…The goal of this note is to show that multiparameter Schur Q-functions Q (a) λ are solutions of BKP hierarchy. The origin for this phenomena lies in the fact proved in [13] that generating functions of multiparameter Schur Q-functions and of classical Schur Q-functions coincide.…”

Section: Introductionmentioning

confidence: 99%

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Multiparameter Schur Q-Functions Are Solutions of the BKP Hierarchy

Rozhkovskaya¹

2019

SIGMA

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Section: Multiparameter Schur Q-functions Are Solutions Of Bkp Hierarchymentioning

confidence: 90%

“…where (−1) σ is the sign of permutation σ ( [13], Proposition 3). Hence, Q (a) α = 0 if α i = α j for some i, j, and for a vector α = (α 1 , .…”

Section: Multiparameter Schur Q-functions Are Solutions Of Bkp Hierarchymentioning

confidence: 99%

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Multiparameter Schur Q-Functions Are Solutions of the BKP Hierarchy

Rozhkovskaya¹

2019

SIGMA

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“…). These interpolation analogues of the classical Schur Q-functions were studied combinatorially in [18,29]. In [47] we proved that multiparameter Schur Q-functions are tau-functions of the BKP hierarchy.…”

Section: [Orv ]mentioning

confidence: 90%

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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“…If the first parameter a 0 is equal to 0, then we can recover Korotkikh's dual P -function (see [7,Definition 2] and (3.8)) given by…”

Section: Factorial P -And Q-functionsmentioning

confidence: 99%

A Generalization of Schur's $P$- and $Q$-Functions

Okada¹

2019

Preprint

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We introduce and study a generalization of Schur's P -/Q-functions associated to a polynomial sequence, which can be viewed as "Macdonald's ninth variation" for P -/Q-functions. This variation includes as special cases Schur's P -/Q-functions, Ivanov's factorial P -/Q-functions and the t = −1 specialization of Hall-Littlewood functions associated to the classical root systems. We establish several identities and properties such as generalizations of Schur's original definition of Schur's Q-functions, Cauchy-type identity, Józefiak-Pragacz-Nimmo formula for skew Q-functions, and Pieri-type rule for multiplication.

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Dual Multiparameter Schur Q-Functions

Cited by 4 publications

References 2 publications

Multiparameter Schur Q-Functions Are Solutions of the BKP Hierarchy

Multiparameter Schur Q-Functions Are Solutions of the BKP Hierarchy

Linear transformations of vertex operator presentations of Hall-Littlewood polynomials

A Generalization of Schur's $P$- and $Q$-Functions

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