The space of generalized G2-theta functions

TL;DR

This paper explores the relationships between generalized G2-theta functions on algebraic curves and classical theta functions, revealing explicit links between these mathematical objects for curves of genus at least 2.

Contribution

It establishes explicit connections between G2-theta functions and classical theta functions for SL_2 and SL_3, expanding understanding of their interrelations.

Findings

Explicit links between G2-theta functions and classical theta functions

Connections established for curves of genus at least 2

Provides new insights into the structure of generalized theta functions

Abstract

Let G2 be the exceptional Lie group of automorphisms of the complex Cayley algebra and C be a smooth, connected, projective curve of genus at least 2. Using the map obtained from extension of structure groups, we prove explicit links between the space of generalized G2-theta functions over C and spaces of generalized theta functions associated to the classical Lie groups SL_2 and SL_3.