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Multiple sums and integrals as neutral BKP tau functions

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 Qα for strict partitions α. We consider two types of such sums: weighted sums of Qα over strict partitions α and sums over products QαQγ. We thus obtain discrete analogues of the beta ensembles (β = 1, 2, 4). Continuous versions are represented as multiple integrals, which are interesting in several problems in mathematics and physics.

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Correspondence to J. Harnad.

Additional information

Prepared from an English manuscript submitted by the authors; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, Vol. 168, No. 1, pp. 112–124, July, 2011.

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Harnad, J., van de Leur, J.W. & Orlov, A.Y. Multiple sums and integrals as neutral BKP tau functions. Theor Math Phys 168, 951 (2011). https://doi.org/10.1007/s11232-011-0077-z

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Keywords

  • integrable system
  • symmetric function
  • projective Schur function
  • random partition