(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Simplify the following expression:

[tex]

\sum_{ \alpha_1 + \cdots + \alpha_n = k} e^{i(\alpha_1 \theta_1 + \cdots + \alpha_n \theta_n)}

[/tex]

2. Relevant equations

[tex]\alpha_n = k - \sum_{j=1}^{n-1} \alpha_j[/tex]

[tex]0 = \sum_{j=1}^{n} \theta_j[/tex]

3. The attempt at a solution

I am trying to simplify the expression above into something a little more manageable. This expression comes from determining the characters of irreps of SU(n), so if that gives anyone ideas on how to simplify this, then any advice would be much appreciated.

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# Homework Help: Simplifying an expression involving complex exponentials

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