Pursuing the double affine Grassmannian II: Convolution

TL;DR

This paper advances the theory of the double affine Grassmannian by proposing a conjectural convolution diagram, extending the geometric framework for affine Kac-Moody groups, with specific insights for G=SL(n).

Contribution

It introduces a conjectural convolution diagram for the double affine Grassmannian, building on prior work and providing a foundation for future geometric and representation-theoretic studies.

Findings

Conjectural convolution diagram proposed for the double affine Grassmannian.

Results consistent with known cases for G=SL(n).

Framework sets stage for further geometric and algebraic exploration.

Abstract

This is the second paper of a series (started by arXiv:0711.2083) 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. In the case when G=SL(n) our conjectures can be derived from arXiv:0809.2605.