Vol. 40, No. 1, 1972

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Defining relations for certain integrally parameterized Chevalley groups

William Patterson Wardlaw

Vol. 40 (1972), No. 1, 235–250

For each faithful finite dimensional irreducible representation R of a finite dimensional simple Lie algebra L over the complex field, this paper treats the integrally parameterized subgroup GZ of the Chevalley Group G over the rational field Q. For L of type Al,Dl, or El, Lie algebraic methods are used to extend a result of J. Nielson on SL(S,Z) to obtain a finite set of defining relations for GZ. Similar relations augmented by defining relations for rτY z(B2) are shown to define GZ when L is of type Bl,Cl, or F4. (The relations for GZ(B2) are not listed here.)

Mathematical Subject Classification 2000
Primary: 20H20
Received: 1 September 1970
Published: 1 January 1972
William Patterson Wardlaw