Construction of p-1 Irreducible Modules with Fundamental Highest Weight for the Symplectic Group in Characteristic p |
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Authors: | Gow Rod |
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Institution: | 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 2mover K. Let V denote the exterior algebra of V and kV its kthexterior power for 0 k 2m. Let f be a non-degenerate alternatingbilinear form defined on VxV. The symplectic group Sp2m(K) isthe group of all isometries of f and it acts as a group of vectorspace automorphisms on kV. In the case that K is algebraicallyclosed and 1 k m, it is known that kV contains a composition factorcorresponding to the fundamental weight k of a root system oftype Cm. We shall refer to the irreducible module for Sp2m(K)given by this composition factor as a fundamental module. |
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