Pfaffian structures and certain solutions to BKP hierarchies II. Multiple integrals

Understand

We introduce a useful and rather simple classes of BKP tau functions which which we shall shall call "easy tau functions".

• We consider the "large BKP hiearchy" related to $O(2\infty +1)$ which was introduced in \cite{KvdLbispec} (which is closely related to the DKP $O(2\infty) $hierarchy introduced in \cite{JM}).
• Actually "easy tau functions" of the small BKP was already considered in \cite{HLO}, here we are more interested in the large BKP and also the mixed small-large BKP tau functions \cite{KvdLbispec}.
• Tau functions under consideration are equal to sums over partitions and to multi-integrals.