Congruence Subgroups and Twisted Cohomology ofSLn(F[t])

✍ Scribed by Kevin P. Knudson

• Book ID: 102577911
• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 291 KB
• Volume: 207
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1006/jabr.1998.7455

✦ Synopsis

In we showed that if F is an infinite field, then the natural inclusion SL n F → SL n F t induces an isomorphism

Here, we study the extent to which this isomorphism holds when the trivial coefficients are replaced by some rational representation of SL n F . The group SL n F t acts on such a representation via the map SL n F t t=0 -→ SL n F . There are two approaches one might take. The first is to use the spectral sequence associated with the action of SL n F t on a certain Bruhat-Tits building χ. With this method, we obtain the following result. Suppose that F is a field of characteristic zero. Let V be an irreducible representation of SL n F .