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Journal of the London Mathematical Society 1998 58(3):619-632; doi:10.1112/S002461079800667X
© 1998 by London Mathematical Society
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© The London Mathematical Society

Construction of p–1 Irreducible Modules with Fundamental Highest Weight for the Symplectic Group in Characteristic p

Rod Gow

Department of Mathematics, University College Belfield, Dublin 4, Ireland

Received 29 October 1996.

Let K be a field and let V be a vector space of dimension 2m over K. Let {wedge}V denote the exterior algebra of V and {wedge}kV its kth exterior power for 0≤k≤2m. Let f be a non-degenerate alternating bilinear form defined on VxV. The symplectic group Sp2m(K) is the group of all isometries of f and it acts as a group of vector space automorphisms on {wedge}kV. In the case that K is algebraically closed and 1≤k≤m, it is known that {wedge}kV contains a composition factor corresponding to the fundamental weight {omega}k of a root system of type Cm. We shall refer to the irreducible module for Sp2m(K) given by this composition factor as a fundamental module.


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