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Pré-Publication, Document De Travail Année : 2010

Some complete intersection symplectic quotients in positive characteristic: invariants of a vector and a covector

Résumé

Given a linear action of a group $G$ on a $K$-vector space $V$, we consider the invariant ring $K[V \oplus V^*]^G$, where $V^*$ is the dual space. We are particularly interested in the case where $V =\gfq^n$ and $G$ is the group $U_n$ of all upper unipotent matrices or the group $B_n$ of all upper triangular matrices in $\GL_n(\gfq)$. In fact, we determine $\gfq[V \oplus V^*]^G$ for $G = U_n$ and $G =B_n$. The result is a complete intersection for all values of~$n$ and~$q$. We present explicit lists of generating invariants and their relations. This makes an addition to the rather short list of ``doubly parametrized'' series of group actions whose invariant rings are known to have a uniform description.
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Dates et versions

hal-00494959 , version 1 (24-06-2010)
hal-00494959 , version 2 (04-04-2011)

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Citer

Cédric Bonnafé, G. Kemper. Some complete intersection symplectic quotients in positive characteristic: invariants of a vector and a covector. 2010. ⟨hal-00494959v1⟩
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