Computing local zeta functions of groups, algebras, and modules

Rossmann, Tobias

doi:10.1090/tran/7361

Computing local zeta functions of groups, algebras, and modules
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by Tobias Rossmann PDF

Trans. Amer. Math. Soc. 370 (2018), 4841-4879 Request permission

Abstract:

We develop a practical method for computing local zeta functions of groups, algebras, and modules in fortunate cases. Using our method, we obtain a complete classification of generic local representation zeta functions associated with unipotent algebraic groups of dimension at most six. We also determine the generic local subalgebra zeta functions associated with $\mathfrak {gl}_2(\mathbf {Q})$. Finally, we introduce and compute examples of graded subobject zeta functions.

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