Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 17 (2021), 001, 26 pages      arXiv:2007.04045      https://doi.org/10.3842/SIGMA.2021.001
Contribution to the Special Issue on Representation Theory and Integrable Systems in honor of Vitaly Tarasov on the 60th birthday and Alexander Varchenko on the 70th birthday

With Wronskian through the Looking Glass

Vassily Gorbounov ab and Vadim Schechtman c
a) HSE University, Russia
b) Laboratory of Algebraic Geometry and Homological Algebra, Moscow Institute of Physics and Technology, Dolgoprudny, Russia
c) Institut de Mathématiques de Toulouse, Université Paul Sabatier, 118 Route de Narbonne, 31062 Toulouse, France

Received September 01, 2020, in final form December 27, 2020; Published online January 02, 2021

Abstract
In the work of Mukhin and Varchenko from 2002 there was introduced a Wronskian map from the variety of full flags in a finite dimensional vector space into a product of projective spaces. We establish a precise relationship between this map and the Plücker map. This allows us to recover the result of Varchenko and Wright saying that the polynomials appearing in the image of the Wronsky map are the initial values of the tau-functions for the Kadomtsev-Petviashvili hierarchy.

Key words: MKP hierarchies; critical points; tau-function; Wronskian.

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