辛展开、平面函数和互正交基
Symplectic spreads, planar functions and mutually unbiased bases
AI总结：
本文通过辛展开和伪平面函数提出新的方法，构造了特殊李代数的正交分解和互正交基的完整集合。
摘要：
本文给出了由交换和辛半场以及某些其他非半场辛展开得到的特殊李代数sl_n(C)的正交分解的完整集合的互正交基(MUBs)的显式描述。还研究了各种构造之间的关系。我们证明了完整MUB集合的自同构群与相应李代数sl_n(C)的正交分解的自同构群同构。在辛展开的情况下，这个自同构群由展开的自同构群确定。通过使用新的伪平面函数概念，我们给出了新的显式MUB集合的构造。
英文摘要：
In this paper we give explicit descriptions of complete sets of mutually unbiased bases (MUBs) and orthogonal decompositions of special Lie algebras $sl_n(\mathbb{C})$ obtained from commutative and symplectic semifields, and from some other non-semifield symplectic spreads. Relations between various constructions are also studied. We show that the automorphism group of a complete set of MUBs is isomorphic to the automorphism group of the corresponding orthogonal decomposition of the Lie algebra $sl_n(\mathbb{C})$. In the case of symplectic spreads this automorphism group is determined by the automorphism group of the spread. By using the new notion of pseudo-planar functions over fields of characteristic two we give new explicit constructions of complete sets of MUBs.
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