论文标题
非交换性Hecke环和Hecke系列的正式电源系列，$ GSP_4 $
A formal power series over a noncommutative Hecke ring and the rationality of the Hecke series for $GSp_4$
论文作者
论文摘要
本论文研究由$ p $ adic Integers的某些代数$ l_p $的自动形态群体衍生而来的Hecke戒指。我们以前的工作考虑了$ l_p $是$ p $ adiC整数的戒指上的海森伯格（Heisenberg Lie Algebra）（尺寸3）。尽管此Hecke环是非交通的，但我们表明，在此Hecke环中具有系数的正式功率系列满足了与Hecke系列的合理性相似的身份，因为E.〜Hecke $ gl_2 $。在本文中，我们在$ p $ adiC整数的戒指上的海森伯格谎言代数为第5位。在这种情况下，由于G.
The present paper studies Hecke rings derived by the automorphism groups of certain algebras $L_p$ over the ring of $p$-adic integers. Our previous work considered the case where $L_p$ is the Heisenberg Lie algebra (of dimension 3) over the ring of $p$-adic integers. Although this Hecke ring is noncommutative, we showed that a formal power series with coefficients in this Hecke ring satisfies an identity similar to the rationality of the Hecke series for $GL_2$ due to E.~Hecke. In the present paper, we establish an analogous result in the case of the Heisenberg Lie algebra of dimension 5 over the ring of $p$-adic integers. In this case, our identity is similar to the rationality of the Hecke series for $GSp_4$, due to G.~Shimura.
