Geodesic
Multiple sums and integrals as neutral BKP tau functions
Teoretičeskaâ i matematičeskaâ fizika, Tome 168 (2011) no. 1, pp. 112-124

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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
Mots-clés : random partition. 
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     author = {J. Harnad and J. W. van de Leur and A. Yu. Orlov},
     title = {Multiple sums and integrals as neutral {BKP} tau functions},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     publisher = {mathdoc},
     volume = {168},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2011_168_1_a8/}
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J. Harnad; J. W. van de Leur; A. Yu. Orlov. Multiple sums and integrals as neutral BKP tau functions. Teoretičeskaâ i matematičeskaâ fizika, Tome 168 (2011) no. 1, pp. 112-124. http://geodesic.mathdoc.fr/item/TMF_2011_168_1_a8/