The superconducting and normal state characteristics of yttrium hexaboride (YB$_6$) have been investigated for the single crystals with a transition temperatures $T_c$ ranging between 6 K and 7.6 K. The extracted set of microscopic parameters [the coherence length $xi$(0) $sim$ 320$div$340 ${AA}$, the penetration depth $lambda$(0) $sim$ 1100$div$1600 ${AA}$ and the mean free path of charge carriers $l$ = 31$div$58 ${AA}$, the Ginzburg-Landau-Maki parameters $kappa$$_{1,2}$(0) $sim$ 3.3$div$4.8 and the superconducting gap $Delta$(0) $sim$ 10.3$div$14.8 K] confirms the type II superconductivity in dirty limit ($xi$$gg$ $l$) with a medium to strong electron-phonon interaction (the electron-phonon interaction constant $lambda_{e-ph}$ = 0.93$div$0.96) and $s$-type pairing of charge carriers in this compound [2$Delta$(0)$/k_BT_c$ $approx$ 4]. The comparative analysis of charge transport (resistivity, Hall and Seebeck coefficients) and thermodynamic (heat capacity, magnetization) properties in the normal state in YB$_6$ allowed to detect a transition into the cage-glass state at $T^*$ $sim$ 50 K with a static disorder in the arrangement of the Y$^{3+}$ ions. We argue that the significant $T_c$ variations in the YB$_6$ single crystals are determined by two main factors: (i) the superconductivity enhancement is related with the increase of the number of isolated vacancies, both at yttrium and boron sites, which leads to the development of an instability in the hexaboride lattice; (ii) the $T_c$ depression is additionally stimulated by the spin polarization of conduction electrons emerged and enhanced by the magnetic field in the vicinity of defect complexes in the YB$_6$ matrix.
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