ORTHOGONAL GROUP of CERTAIN INDEFINITE LATTICE Chang Heon Kim* 1. Introduction Given an Even Lattice M in a Real Quadratic Space

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JOURNAL OF THE CHUNGCHEONG MATHEMATICAL SOCIETY Volume 20, No. 1, March 2007

Chang Heon Kim*

Abstract. We compute the special orthogonal group of certain lattice of signature (2 1).

−

0
0

≈
×

Theorem

integral symmetric matrices, that is,

. Let
be a 3-dimensional even lattice of all

Received December 30, 2006. 2000 Mathematics Subject Classiﬁcation: Primary 11F03, 11H56. Key words and phrases: indeﬁnite lattice, orthogonal group. * This work was supported by a Bahrom research grant from Seoul Women’s
University (2007).

48
Chang Heon Kim

with norm special orthogonal group of ) is isomorphic to

−

for

∈

. Then
(=the

Remark
.

∗

0
0

∈
∈

1 0 0 0
0 1 1 0
0 0 0 1
1 0 0 1

∈

3
100
010
001
2

−

−
−
−

Orthogonal group of certain indeﬁnite lattice
49

−
×−

−

22
22

[1]

R. Borcherds, Automorphic forms with singularities on Grassmanians, Invent.

Math. 132 (1998), 491-562.

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