What's the purpose of this LRC in this xover?

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This would have put a slight notch at around 2KHZ if there had been a series resistance between the amplifier and the crossover, but there isn't as you show it. More likely it presents a shunt 10 ohm resistance at the crossover frequency to keep the whole speaker's impedance from peaking too high at that point and developing too large a reactive phase angle (which might upset some amps). Only conjecture since you didn't show the rest of the speaker.
 
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