Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Congruence subgroups and twisted cohomology of SL_n(F[t])   Let F be a field of characteristic zero and let V be an irreducible
representation of SL_n(F). In this paper, we compute the first cohomology of
SL_n(F[t]) with coefficients in V. It agrees with H^1(SL_n(F),V) if V is not
the adjoint representation, while if V = Ad, the two groups differ by an
F-vector space X. We show that if n=2, X is infinite dimensional, while if n>2,
dim X = 1. We also study the abelianization of the kernel of the map
SL_n(F[t])-->SL_n(F) given by setting t=0, where now F is any field. We
conjecture that this abelianization is the adjoint representation sl_n(F) if
n>2 and F is finite, and prove this in the case n=3, F=F_2, F_3.

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The categories of this paper are: cond-mat
33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
1
The categories of this paper are: cs
17
The categories of this paper are: q-fin
16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph
23
The categories of this paper are: solv-int
27
The categories of this paper are: comp-gas
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The categories of this paper are: quant-ph
24
The categories of this paper are: dg-ga
31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
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The categories of this paper are: nlin
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The categories of this paper are: hep-ex