科研进展

论文题目:Enhanced variety of higher level and Kostka functions associated to complex reflection groups

论文作者:Toshiaki Shoji

发表刊物:Transformation Groups

成果介绍:Let V be an n-dimensional vector space over an algebraic closure of a finite field F q , and G = GL(V). A variety https://static-content.springer.com/image/art%3A10.1007%2Fs00031-017-9422-0/MediaObjects/31_2017_9422_Figa_HTML.gif https://static-content.springer.com/image/art%3A10.1007%2Fs00031-017-9422-0/MediaObjects/31_2017_9422_Figa_HTML.gif is called an enhanced variety of level r. Let https://static-content.springer.com/image/art%3A10.1007%2Fs00031-017-9422-0/MediaObjects/31_2017_9422_Figb_HTML.gif https://static-content.springer.com/image/art%3A10.1007%2Fs00031-017-9422-0/MediaObjects/31_2017_9422_Figb_HTML.gifbe the unipotent variety of https://static-content.springer.com/image/art%3A10.1007%2Fs00031-017-9422-0/MediaObjects/31_2017_9422_Figc_HTML.gif https://static-content.springer.com/image/art%3A10.1007%2Fs00031-017-9422-0/MediaObjects/31_2017_9422_Figc_HTML.gif . We have a partition https://static-content.springer.com/image/art%3A10.1007%2Fs00031-017-9422-0/MediaObjects/31_2017_9422_Figd_HTML.gif https://static-content.springer.com/image/art%3A10.1007%2Fs00031-017-9422-0/MediaObjects/31_2017_9422_Figd_HTML.gif indexed by r-partitions λ of n In the case where r = 1 or 2, X λ is a single G-orbit, but if r3,X λ is, in general, a union of infinitely many G-orbits. In this paper, we prove certain orthogonality relations for the characteristic functions (over F q ) of the intersection cohomology IC(X¯λ,Q¯l), and show some results, which suggest a close relationship between those characteristic functions and Kostka functions associated to the complex reflection group https://static-content.springer.com/image/art%3A10.1007%2Fs00031-017-9422-0/MediaObjects/31_2017_9422_Fige_HTML.gif https://static-content.springer.com/image/art%3A10.1007%2Fs00031-017-9422-0/MediaObjects/31_2017_9422_Fige_HTML.gif

所属学科:基础数学

论文地址:https://link.springer.com/article/10.1007%2Fs00031-017-9422-0

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