Does income inequality slow economic growth?

There are many schools of thought associated with this question, but I am going to focus on general principles taught in introductory economics classes.

The truth is that the answer is "it depends".  Generally income inequality means that more resources are allocated to certain individuals in the economy than to others.  For example, rich people are rich because they control many resources. If the rich earned the right to the resources (by paying for them and using them efficiently) then the resources are allocated efficiently.  Efficiency in this context means that someone who can use the resource the best, has access to it.  So it makes sense for a rich person to manage money, obviously they are good at it or they would not be rich.  Likewise, people who are good at digging for gold or cutting hair have resources that specialize in those tasks allocated to them.  This may make them "poor" but these "poor" resources have been allocated to them for a reason (meaning they could afford it and they know how to use it).
However, if income inequality is due to corruption or other non-market based reasons it can hamper growth.  For example, if a rich person is rich because he is good at stealing or because his parents were rich this can lead to inefficiency.  Imagine a famous software engineer giving his billion dollar company to his son, these resources were allocated to him in a non-market context.  The son did not pay market value for the resources so potentially he is not the best person in the economy to manage them.  This type of inequality would hamper economic growth. 

Another example is corruption.  Imagine a government employee overlooking a farmer.  The farmer owns the land and contributes to the economy but the corrupt government worker sells fake permits to allow the farmer to farm.  The government employee gets rich, but contributes nothing to the economy, in fact he is preventing the farmer from investing in capital improvements to potentially improve the economy.

Generally, questions like this lead back to the efficiency vs fairness argument which I am not qualified (nor is anyone really) to answer.