Multiple sums and integrals as neutral BKP tau functions

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.

16 pages

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Cited by in corpus (5)

• Superintegrability of Kontsevich matrix model
• Cut-and-join structure and integrability for spin Hurwitz numbers
• Around spin Hurwitz numbers
• Matrix model for the total descendant potential of a simple singularity of type $D$
• Notes about KP/BKP correspondence