论文标题
对称函数和弹簧表示
Symmetric functions and Springer representations
论文作者
论文摘要
Kazhdan [以色列J. Math。 {\ bf 28}（1977）]，后者用Hall-Littlewood的$ Q $ functions by Green [Trans。阿米尔。数学。 Soc。 （1955）]。在本文中，我们提供了一个纯粹的代数证明，即$ \ mathop {gl}（n）$的（总）弹簧表示是$ \ mathrm {ext} $ - 彼此之间的正交形式，并表明它与对称函数环的自然分类兼容。
The characters of the (total) Springer representations are identified with the Green functions by Kazhdan [Israel J. Math. {\bf 28} (1977)], and the latter are identified with Hall-Littlewood's $Q$-functions by Green [Trans. Amer. Math. Soc. (1955)]. In this paper, we present a purely algebraic proof that the (total) Springer representations of $\mathop{GL} ( n )$ are $\mathrm{Ext}$-orthogonal to each other, and show that it is compatible with the natural categorification of the ring of symmetric functions.
