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| A New Prehomogeneous Vector Space of Characteristic p |
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Citation： |
Chen Zhijie.A New Prehomogeneous Vector Space of Characteristic p[J].Chinese Annals of Mathematics B,1987,8(1):22~35 |
| Page view： 906
Net amount： 794 |
Authors： |
Chen Zhijie; |
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| Abstract： |
Let K be an algebraically closed field of characteristic 3. Let \Lambda_1,\Lambda_2,\Laambda_3 denote all: the fundamental dominant weights of GL(4). Then the K-dimension of the irreducible GL(4)- module V with the highest weight \Lambda_1 +\Lambda_2 is equal to 16, and it is denoted , by V(16). In this paper, the following results are proved:
(1) (GL(4),\Lambda_1 +\Lambda_2 ,V(16)) is a regular irreducible prehomogeneous vector space.The degree of its irreducible relative invariant is 8, the associated character is
X(g) = (det g)^6.
(2) There exist only one 6-dimensional GL (4) -orbit and one 9-dimensional GL(4)- orbit in V(16). When m=7, 8 or l\leq m\leq 5, there are no m-dimensional GL(4)-orbits. |
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