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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.

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  • $\begingroup$ Yes, in particular for $\mathfrak{sl}_2(\Bbb C)$, see page $5$ here. $\endgroup$ – Dietrich Burde Mar 11 at 12:57
  • $\begingroup$ Seems like it uses Weyl character formula and gives a consequence of that in case of $sl_2\mathbb{C}$ $\endgroup$ – justanothermathstudent Mar 11 at 13:13
  • $\begingroup$ 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. $\endgroup$ – Dietrich Burde Mar 11 at 15:54

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