i was wondering what the irreducible $\displaystyle gl(2)$-module $\displaystyle V((\lambda_1, \lambda_2))$ is?
when posting a question, you need to explain your notation clearly so we know what you're talking about. we are not inside your head!!
anyway, i guess you're talking about modules over Lie algebras? you didn't say anything as if we were your classmates!!
"irreducible" means simple, i.e. your module has no non-trivial submodule.
yes modules over Lie Algebras
$\displaystyle gl(2)$ has basis $\displaystyle \{a^1_1, a^1_2, a^2_1, a^2_2\}$
i have to find constraints $\displaystyle \lambda_1$ and $\displaystyle \lambda_2$ such that the irreducible $\displaystyle gl(2)$-module $\displaystyle V((\lambda_1, \lambda_2))$ has dimension $\displaystyle n$...any ideas?