科研之友
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摘要
Let F be a field, V a 6-dimensional F-vector space and f a nondegenerate alternating bilinear form on V. We consider a 14-dimensional module for the symplectic group Sp(V, f) congruent to Sp(6, F) associated with (V, f), and classify the orbits on vectors. For characteristic distinct from 2, this module is irreducible and isomorphic to the Weyl module of Sp(V, f) for the fundamental weight lambda(3). If the characteristic is 2, then the module is reducible as it contains an 8-dimensional submodule isomorphic to the spin module of Sp(V, f).
- 出版日期2015
