User:TakuyaMurata/Representation theory notes

Basics
This is testing. Regular ring

Parametrization of a basis
Let $$G_i = \operatorname{GL} (n-i, \mathbb{C})$$. We have the following decreasing filtration of subgroups:
 * $$G_0 \supset G_1 \supset \cdots \supset G_{n-1} = \mathbb{G}_m$$

such that $$G_{n-1} \hookrightarrow G_{n-2}, g \mapsto \operatorname{diag}(g, 1)$$ and so forth.