Abstract
Let K be the subgroup of SL n (F[t]) consisting of matrices congruent to the identity modulo t. In Citation[7], the author conjectured that if F is a finite field, then H 1(K) is the adjoint representation s l n (F). A proof of this conjecture is provided in this note. The argument also works in case F is a number field. Applications to the cohomology of SL n (F[t]) are included as is the study of the analogous question for SL n (F[t, t −1]).
ACKNOWLEDGMENT
Supported by NSF grant DMS-0070119.