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Information Center for Mathematical Science

논문검색

Information Center for Mathematical Science

논문검색

Journal of Pure and Applied Algebra
( Vol. 112 NO.1 / (1996))
2-Dimensional vector invariants of parabolic subgroups of $Gl_2(F_p)$ over the field $F_p^1$
H. E. A. Campbell, I. P. Hughes,
Pages. 1-12
Abstract Given a group $G$ acting on a finite dimensional vector space $V$ over
any field $K$, we ask for the structure of the ring of invariants of the
diagonal action of the group on the symmetric algebra of $m$ a copies of $V$,
the so-called $m$-dimensional vector invariants of $G$. In this paper we use
elementary techniques to determine the structure of the 2-dimensional vector
invariants of $Gl_2(F_p), Sl_2(F_p), U_2(F_p)$ acting as usual on a vector
space of dimension 2 over $F_p$. We know that these rings of invariants are
Cohen-Macaulay and we compute for each a free module basis over a suitably
chosen homogeneous system of parameters.
Contents 1. Introduction
2. 2-dimension vector invariants of $P$ recalled
3. Getting ready
4. 2-dimensional vector invariants of $U=U_2(F_p)$
5. 2-dimensional vector invariants of $S=Sl_2(F_p)$
6. 2-dimensional vector invariants of $G=Gl_2(F_p)$
Acknowledgements
Key words
Mathmatical Subject Classification