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arXiv · 1101.4216

Multiple sums and integrals as neutral BKP tau functions

J. Harnad·J. W. van de Leur·A. Yu. Orlov
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Abstract

We consider multiple sums and multi-integrals as tau functions of the BKP hierarchy using neutral fermions as the simplest tool for deriving these. The sums are 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 $Q_\alpha Q_\gamma$. In this way we obtain discrete analogues of the beta-ensembles ($\beta=1,2,4$). Continuous versions are represented as multiple integrals. Such sums and integrals are of interest in a number of problems in mathematics and physics.

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J. Harnad, J. W. van de Leur, A. Yu. Orlov. 2011-01-21. Multiple sums and integrals as neutral BKP tau functions. https://doi.org/10.1007/s11232-011-0077-z

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