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Transformation Groups

, Volume 22, Issue 3, pp 793–844 | Cite as

ENHANCED VARIETY OF HIGHER LEVEL AND KOSTKA FUNCTIONS ASSOCIATED TO COMPLEX REFLECTION GROUPS

  • TOSHIAKI SHOJI
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Abstract

Let V be an n-dimensional vector space over an algebraic closure of a finite field F q , and G = GL(V). A variety Open image in new window is called an enhanced variety of level r. Let Open image in new window be the unipotent variety of Open image in new window . We have a partition Open image in new window indexed by r-partitions λ of n In the case where r = 1 or 2, X λ is a single G-orbit, but if r ≥ 3, 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 \( \mathrm{I}\mathrm{C}\left({\overline{X}}_{\boldsymbol{\uplambda}},{\overline{\mathbf{Q}}}_l\right) \), and show some results, which suggest a close relationship between those characteristic functions and Kostka functions associated to the complex reflection group Open image in new window .

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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.Department of MathematicsTongji UniversityShanghaiP.R. China

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