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Interband transitions in a narrow-gap InSb cylindrical quantum dot (QD) have been theoretically studied in the regime of strong dimensional quantization with allowance for a nonparabolic dispersion of electrons and light holes. The corresponding absorption coefficients and threshold frequencies for a QD array are calculated within the framework of a two-band Kane model for electrons and light holes and a parabolic dispersion law for heavy holes. These threshold frequencies fall in the IR range. Quantitative calculations are performed using the recent data of Moiseev et al. [1] on the growth of InSb quantum dots by liquid phase epitaxy. [ABSTRACT FROM AUTHOR]