Homological stability for certain classical groups

We prove homological stability for standard unitary groups over R, C and H and for general linear groups over skew-fields with infinite centre. We focus on the similarities and differences of these proofs. Both proofs are due to Chih-Han Sah (Homology of classical Lie groups made discrete I: Stability theorems and Schur multipliers. Comment. Math. Helv. 61(2), 1986).

💡 Research Summary

The thesis “Homological stability for certain classical groups” (Jan Essert, 2006) presents a detailed exposition of homological stability results for two families of classical groups, following the original proofs of Chih‑Han Sah (Comment. Math. Helv. 61 (1986)). The two families are: (i) general linear groups (GL_n(F)) over a skew‑field (F) whose centre is infinite, and (ii) standard unitary groups (U_n(\mathbb{K})) over the real numbers, complex numbers, and quaternions ((\mathbb{K}=\mathbb{R},\mathbb{C},\mathbb{H})). The central question is: for the natural inclusion \