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CONSTRUCTION OF p−1 IRREDUCIBLE MODULES WITH FUNDAMENTAL HIGHEST WEIGHT FOR THE SYMPLECTIC GROUP IN CHARACTERISTIC p

Published online by Cambridge University Press:  01 December 1998

ROD GOW
Affiliation:
Department of Mathematics, University College, Belfield, Dublin 4, Ireland
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Abstract

Let K be a field and let V be a vector space of dimension 2m over K. Let ∧V denote the exterior algebra of V and ∧kV its kth exterior power for 0[les ]k[les ]2m. Let f be a non-degenerate alternating bilinear form defined on V×V. The symplectic group Sp2m(K) is the group of all isometries of f and it acts as a group of vector space automorphisms on ∧kV. In the case that K is algebraically closed and 1[les ]k[les ]m, it is known that ∧kV contains a composition factor corresponding to the fundamental weight ωk 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.

Type
Notes and Papers
Copyright
The London Mathematical Society 1998

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