Multiple sums and integrals as neutral BKP tau functions

Details Multiple sums and integrals as neutral BKP tau functions Multiple sums and integrals as neutral BKP tau functions

2011-01-21

arxiv.org/abs/1101.4216v1

Theor.Math.Phys.168:951-962,2011

Physics

Mathematical Physics

16 pages

Scientific paper

10.1007/s11232-011-0077-z

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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