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The results of the optical properties study and the electronic structure calculation of ${\text{Co}}_{2}Y\text {Si}$ ($Y = \text {Ti}$ , V, Cr, Mn, Fe) Heusler alloys are presented. Temperature dependences of the electrical resistivity were studied in the temperature range from 4.2 to 300 K. Field dependences of magnetization were measured in the magnetic fields of up to 5 T. The main attention is paid to the spectral dependence of the real and imaginary parts of the dielectric constant in the wavelength range from 0.3 to $8~\mu \text{m}$ by the ellipsometric Beattie method at room temperature. Anomalous behavior of optical conductivity at infrared (IR) frequencies in Co2TiSi and Co2VSi alloys was found, which significantly differs from that in Co2MnSi, Co2FeSi, and Co2CrSi. The results obtained are discussed based on calculations of the electronic structure. Simultaneously, the correlations between the changes in these characteristics can be an indicator of the states of a half-metallic ferromagnet (HMF) or a spin gapless semiconductor (SGS). A high degree of charge carriers’ spin polarization is possible in such materials, and therefore, they are promising materials for spintronics. [ABSTRACT FROM AUTHOR]