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In this note, we remark on the range in Borel's theorem on the stablecohomology of the arithmetic groups Sp(2n,Z) and SO(n,n;Z). This improves therange stated in Borel's original papers, an improvement that was known toBorel. Our main task is a technical computation involving the Weyl group actionon roots and weights. This note originally appeared as the appendix toarXiv:1711.03139.

Borel's stable range for the cohomology of arithmetic groups