Multiple sums and integrals as neutral BKP tau functions

作者：Harnad J^*; van de Leur J W; Orlov A Yu

来源：Theoretical and Mathematical Physics, 2011, 168(1): 951-962.

DOI：10.1007/s11232-011-0077-z

• integrable system
• symmetric function
• projective Schur function
• random partition

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.

• 出版日期2011-7