Denominators for one variable Poincaré series of generic matrices

We study the Poincaré series of the mixed and pure trace rings of generic matrices. These series are known to be rational functions. We obtain an explicit formula in lowest terms in the case of 2×2 matrices; a denominator, which we presume but have not been able to prove to be in lowest terms, in th...

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Vydáno v:Journal of algebra Ročník 618; s. 195 - 213
Hlavní autor: Berele, Allan
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier Inc 15.03.2023
Témata:
Invariants of matrices
Poincaré series
Trace rings of generic matrices
Trace rings of generic matrices
Invariants of matrices
Poincaré series
ISSN:0021-8693, 1090-266X
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Shrnutí:We study the Poincaré series of the mixed and pure trace rings of generic matrices. These series are known to be rational functions. We obtain an explicit formula in lowest terms in the case of 2×2 matrices; a denominator, which we presume but have not been able to prove to be in lowest terms, in the case of 3×3 matrices; and a conjectured denominator in the general case.
ISSN:0021-8693
1090-266X
DOI:10.1016/j.jalgebra.2022.11.023