# Proof of Weyl Character formula for $sl_n\mathbb{C}$

Is there a proof of Weyl character formula just for $$sl_n\mathbb{C}$$ independent of any 'heavy machinery'? Please suggest some references if possible.

• Yes, in particular for $\mathfrak{sl}_2(\Bbb C)$, see page $5$ here. – Dietrich Burde Mar 11 at 12:57
• Seems like it uses Weyl character formula and gives a consequence of that in case of $sl_2\mathbb{C}$ – justanothermathstudent Mar 11 at 13:13
• Yes, that's right. But then one has an easy version for $\mathfrak{sl}_2(\Bbb C)$, which can be proved directly without heavy machinery. – Dietrich Burde Mar 11 at 15:54