Abelian variety and spin representation ∗
Abelian variety and spin representation ∗
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阿贝尔簇和自旋表示*
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发表时间：
1999
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通讯作者：
S. Mukai
中科院分区：
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作者：
S. Mukai
阿贝尔簇和 K3 曲面的对称性大于其自同构。我们通过对它们的向量丛的研究了解到了这一点。这种现象与函数空间 L2(R) 上的元合群的作用以及李的球体几何相似。在本文中，扩展 [M2] 中定义的傅里叶函子，我们将证明酉群 U(X × X̂) 作用于复数阿贝尔簇模移位的派生范畴 Dc(X)（定理 1.14）。此外，使用自旋表示（§2），我们将证明双覆盖群 USpin(X × X̂) 具有更精细的作用。陈省身特征图和黎曼-罗赫定理在该群作用上是等变的 (§3)。该作用将由半齐次向量丛（或其通用族）构造，代替庞加莱线丛（§4）。在第 5 节中，我们证明李群 U(X × X̂)R 是 Hermitian 类型，并且自等价群 U(X × X̂) 作用于管域
Abelian varieties and K3 surfaceshave bigger symmetry than their automorphisms. We have learned this from the study of vector bundles on them. This phenomenon is similar to the action of metaplectic group on the function space L2(R) and to sphere geometry of Lie. In this article, extending the Fourier functor defined in [M2], we shall show that a unitary group U(X × X̂) acts on the derived category Dc(X) of an abelian variety modulo shift of complex (Theorem 1.14). Moreover, using the spin representations (§2), we shall show that a double covering group USpin(X × X̂) has a finer action. The Chern character map and Riemann-Roch theorem are equivariant on this group action (§3). The action will be constructed by semi-homogeneous vector bundles (or their universal family), in place of the Poincaré line bundle (§4). In §5, we show that the Lie group U(X × X̂)R is of Hermitian type and that the group U(X × X̂) of autoequivalences acts on the tube domain