A sequence of \(S_n\)-representations \(\{V_n\}\) is said to be uniformly representation stable if the decomposition of \(V_n = \bigoplus _{\mu } c_{\mu ,n} V(\mu )_n\) into irreducible representations is independent of n for each \(\mu \)—that is, the multiplicities \(c_{\mu ,n}\) are eventually independent of n for each \(\mu \). Church–Ellenberg–Farb proved that the cohomology of flag varieties (the so-called diagonal coinvariant algebra) is uniformly representation stable. We generalize their result from flag varieties to all Springer fibers. More precisely, we show that for any increasing subsequence of Young diagrams, the corresponding sequence of Springer representations form a graded co-FI-module of finite type (in the sense of Church–Ellenberg–Farb). We also explore some combinatorial consequences of this stability.

如果\（V_n = \ bigoplus _ {\ mu} c _ {\ mu，n} V（的分解）被称为\（S_n \） -表示\（\ {V_n \} \）的序列是一致表示稳定的。 \亩）_n \）成不可约表示为独立的ñ每个\（\亩\），也就是说，在多重性\（C _ {\亩，N} \）是最终独立的ñ每个\（\亩\ ）。Church–Ellenberg–Farb证明了旗标变种（所谓的对角协变代数）的同调性始终表示稳定。我们将其结果从标志品种推广到所有Springer纤维。更确切地说，我们表明，对于任何增加的Young图子序列，Springer表示的相应序列形成了有限类型的分级co-FI模块（在Church-Ellenberg-Farb的意义上）。我们还探讨了这种稳定性的一些组合后果。