Pursuing the double affine Grassmannian III: Convolution with affine Zastava

TL;DR

This paper advances the theory of the double affine Grassmannian by proposing a conjectural convolution diagram for affine Zastava, extending the geometric framework for affine Kac-Moody groups.

Contribution

It introduces a conjectural convolution diagram for the double affine Grassmannian and affine Zastava, building on previous work to deepen the geometric understanding of affine Kac-Moody groups.

Findings

Proposes a conjectural convolution diagram for the double affine Grassmannian.

Extends the geometric framework for affine Zastava.

Builds on prior conjectures to deepen the understanding of affine Kac-Moody groups.

Abstract

This is the third paper of a series (started by arXiv:0711.2083, arXiv:0908.3390) which describes a conjectural analog of the affine Grassmannian for affine Kac-Moody groups (also known as the double affine Grassmannian). The current paper is dedicated to describing a conjectural analog of the convolution diagram for the double affine Grassmannian and affine Zastava.