Geodesic
Invariant lattices in the~Steinberg module and their isometry groups
Sbornik. Mathematics, Tome 80 (1995) no. 2, pp. 519-529

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The main goal of this paper is the investigation of invariant lattices and the computation of their isometry groups when $G=\operatorname{SL}(2,q)$ and $V$ is the Steinberg module. 
@article{SM_1995_80_2_a13,
     author = {V. P. Burichenko},
     title = {Invariant lattices in {the~Steinberg} module and their isometry groups},
     journal = {Sbornik. Mathematics},
     pages = {519--529},
     publisher = {mathdoc},
     volume = {80},
     number = {2},
     year = {1995},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1995_80_2_a13/}
}
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V. P. Burichenko. Invariant lattices in the~Steinberg module and their isometry groups. Sbornik. Mathematics, Tome 80 (1995) no. 2, pp. 519-529. http://geodesic.mathdoc.fr/item/SM_1995_80_2_a13/