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TMF, 2011, Volume 168, Number 1, Pages 112–124 (Mi tmf6667)  

This article is cited in 2 scientific papers (total in 2 papers)

Multiple sums and integrals as neutral BKP tau functions

J. Harnadab, J. W. van de Leurc, A. Yu. Orlovd

a Centre de recherches mathématiques, Université de Montréal, Montréal, Canada
b Department of Mathematics and Statistics, Concordia University, Montréal, Canada
c Mathematical Institute, University of Utrecht, Utrecht, The Netherlands
d Институт океанологии, Москва, Россия

Abstract: We consider multiple sums and multiple integrals as tau functions of the so-called neutral Kadomtsev–Petviashvili hierarchy on a root lattice of type B; neutral fermions, as the simplest tool, are used to derive them. The sums are taken over projective Schur functions $Q_\alpha$ for strict partitions $\alpha$. We consider two types of such sums: weighted sums of $Q_\alpha$ over strict partitions $\alpha$ and sums over products $Q_\alpha Q_\gamma$. We thus obtain discrete analogues of the beta ensembles $(\beta=1,2,4)$. Continuous versions are represented as multiple integrals, which are interesting in several problems in mathematics and physics.

Keywords: integrable system, symmetric function, projective Schur function, random partition

DOI: https://doi.org/10.4213/tmf6667

Full text: PDF file (489 kB)
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English version:
Theoretical and Mathematical Physics, 2011, 168:1, 951–962

Bibliographic databases:

Document Type: Article

Citation: J. Harnad, J. W. van de Leur, A. Yu. Orlov, “Multiple sums and integrals as neutral BKP tau functions”, TMF, 168:1 (2011), 112–124; Theoret. and Math. Phys., 168:1 (2011), 951–962

Citation in format AMSBIB
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\paper Multiple sums and integrals as neutral BKP tau functions
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\pages 112--124
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\jour Theoret. and Math. Phys.
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\pages 951--962
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Johan W. van de Leur, Alexander Yu. Orlov, Takahiro Shiota, “CKP hierarchy, bosonic tau function and bosonization formulae”, SIGMA, 8 (2012), 036, 28 pp.  mathnet  crossref  mathscinet
    2. van de Leur J.W. Orlov A.Yu., “Character Expansion of Matrix Integrals”, J. Phys. A-Math. Theor., 51:2 (2018), 025208  crossref  mathscinet  zmath  isi  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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