标题： 经典插值范畴 显示英文标题

标题： Classical interpolation categories

摘要： 我们研究可以解释有限经典群表示范畴的张量范畴。 至少有两种方法可以研究这些范畴：通过超积和通过寡态群。 这两种方法各有优缺点。 超积范畴易于定义，但其结构不清晰。 另一方面，寡态方法需要某种类型的测度作为输入，而测度空间并不明显。 此外，不能预先确定这两种方法在一般情况下是否产生相同的范畴。 我们解决了所有这些问题：我们确定了寡态群上的所有测度，并证明了寡态和超积范畴是一致的，这为我们提供了后者的基本结构结果。 我们的结果依赖于（在某种意义上重新整理了）有限几何中的枚举结果。 显示英文摘要

摘要： We study tensor categories that interpolate the representation categories of finite classical groups. There are (at least) two ways to approach these categories: via ultraproducts and via oligomorphic groups. Both have strengths and weaknesses. The ultraproduct categories are easy to define, but their structure is not clear. On the other hand, the oligomorphic approach requires a certain kind of measure as an input, and the space of measures is not obvious. Furthermore, it is not a priori clear that the two approaches yield the same categories in general. We handle all of these issues: we determine all measures on the oligomorphic groups, and we show that the oligomorphic and ultraproduct categories agree, which gives us basic structural results about the latter. Our results rely upon (and in some sense repackage) enumerative results in finite geometry.