Some geometric consequences of the symmetric reduction

Taiwang Deng

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arXiv · 2404.00759

Some geometric consequences of the symmetric reduction

Taiwang Deng

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Abstract

In this article, we derived some consequences to the symmetrization process developed in \cite{Deng23}. This consists a geometric derivation of part of the properties which uniquely determines the Kazhdan-Lusztig polynomials of type $A_n$ as well as an interpretations of the last property by the decomposition theorem of \cite{BBD}. Finally, the relation of geometry of graded nilpotent classes to Parabolic Kazhdan-Lusztig polynomials is discussed for the purpose of later applications to Zelevinsky's derivatives.

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Taiwang Deng. 2024-03-31. Some geometric consequences of the symmetric reduction. https://arxiv.org/abs/2404.00759

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