Анонсы

Abstract

Flows consisting of generalized convolution symmetries are shown to give rise to an alternative fermionic operator representation of Tau functions for the KP-chain and 2KP-Toda hierarchies. The relation between such flows and the usual ones is examined, both in the first quantized and second quantized frameworks. (A rapid review will be given of the Sato, Jimbo, Miwa fermionic constructions of Tau functions.) Examples that are explained by this approach include: recent work of Okounkov and Pandharipande on generating functions for equivariant Gromov-Witten invariants and Hurwitz numbers; generating functions for Melting Crystals, (Reshetikhin; Natkatsu and Takahashi ) and recent results of Abanov, Bettelheim, and Wiegmann on electronic correlators. (This is based on joint work with A. Yu. Orlov)