# Tagged Questions

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### Complex Finite Dimensional Representation of GL(N,C)

What are all the complex finite dimensional linear representation of $GL(N,\mathbb{C})$?
We already know all the complex finite dimensional linear representation of SU(N).

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**2**answers

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### Symmetric and Exterior products of sl(n,C)-module

Let M be the $sl(n,C)$-representation of the inclusion $sl(n,C)\hookrightarrow gl(n,C)$.
Let q be a symbol.
$f(q)=1-M q + \wedge^2Mq^2-...+(-1)^n\wedge^nMq^n$
$g(q)=\sum_{i=0}^\infty Sym^iM \; q^i$
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### Langlands Dual Groups

Can someone explain, explicitly, how to, given a reductive complex algebraic group construct the Langlands dual group? I know it is a group with the cocharacters of G as its characters, but how does ...