5
votes
1answer
216 views

Index of congruence modular subgroup of level (1,d)

Let $D = \text{diag}(1,d)\in M_{2}(\mathbb{Z})$ be a $2\times 2$ matrix, where $d$ is an odd integer. We define the subgroup $\Gamma_D\subset M_{4}(\mathbb{Z})$ as: $$\Gamma_D := \left\lbrace R\in ...
19
votes
1answer
721 views

Conformal blocks vector bundles on $\overline{M}_{g}$ in terms of generalized theta functions?

Conformal field theory uses representation theory to produce various vector bundles on the Deligne-Mumford compactified moduli spaces $\overline{M}_{g}$ and $\overline{M}_{g,n}$, known as bundles of ...
2
votes
1answer
613 views

Theta Functions and Cousins

So I am (barely) familiar with the construction of the theta function of an integral lattice $L$. The theta function, as I understand it, is defined as the function which takes a variable $z$ and ...