irreducible gl(2)-module

**wik_chick88** · September 22nd 2011, 05:31 PM

i was wondering what the irreducible $gl(2)$ -module $V((\lambda_1, \lambda_2))$ is?

**NonCommAlg** · September 22nd 2011, 06:21 PM

Originally Posted by wik_chick88

i was wondering what the irreducible $gl(2)$ -module $V((\lambda_1, \lambda_2))$ 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.

**wik_chick88** · September 22nd 2011, 08:01 PM

yes modules over Lie Algebras
$gl(2)$ has basis $\{a^1_1, a^1_2, a^2_1, a^2_2\}$

i have to find constraints $\lambda_1$ and $\lambda_2$ such that the irreducible $gl(2)$ -module $V((\lambda_1, \lambda_2))$ has dimension $n$ ...any ideas?

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