An inclusion between sets of orbits and surjectivity of the restriction map of rings of invariants
An inclusion between sets of orbits and surjectivity of the restriction map of rings of invariants
复制标题
不变量环限制图的轨道组和满射性之间的包含
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发表时间：
2008
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通讯作者：
Takuya Ohta
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作者：
Takuya Ohta
设V是复数域C上的有限维向量空间，通过伴随作用，GL(V)的一个约化子群G作用在End(V)的一个子空间L上，G的一个闭子群作用在L的一个子空间L上.本文给出了包含(G，L)→(G，L)轨道对应L/G→L/G(0→O：=Ad(G))的一个充分条件.O)是内射的。进一步证明了L上的G-不变量环C[L]G是C[L]G|L在其商域上的积分闭包。然后，如果环C[L]G|L是正规的，则限制映射REST：C[L]G→C[L]G(f→f[L)是满射的。在此基础上，我们给出了L/G→L/G是内射且其余的例子：C[L]G→c[L]G是满射。
Let V be a finite dimensional vector space over the complex number field C. Suppose that, by the adjoint action, a reductive subgroup G of GL(V) acts on a subspace L of End(V) and a closed subgroup G of G acts on a subspace L of L. In this paper, we give a sufficient condition on the inclusion (G, L) → (G, L) for which the orbits correspondence L/G → L/G (0 →O:= Ad(G). O) is injective. Moreover we show that the ring C[L] G of G-invariants on L is the integral closure of C[L] G |L in its quotient field. Then, if the ring C[L] G |L is normal, the restriction map rest: C[L] G → C[L] G (f → f[ L ) is surjective. By using this, we give some examples for which L/G → L/G is injective and rest: C[L] G → c[L] G is surjective.