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• W2340891951 abstract "We study for each $n$ a one-parameter family of complex-valued measures on the symmetric group $S_n$, which interpolate the probability of a monic, degree $n$, square-free polynomial in $mathbb{F}_q[x]$ having a given factorization type. For a fixed factorization type, indexed by a partition $lambda$ of $n$, the measure is known to be a Laurent polynomial. We express the coefficients of this polynomial in terms of characters associated to $S_n$-subrepresentations of the cohomology of the pure braid group $H^{bullet}(P_n, mathbb{Q})$. We deduce that the splitting measures for all parameter values $z= -frac{1}{m}$ (resp. $z= frac{1}{m}$), after rescaling, are characters of $S_n$-representations (resp. virtual $S_n$-representations.)" @default.
• W2340891951 created "2016-06-24" @default.
• W2340891951 creator A5005612207 @default.
• W2340891951 creator A5027533154 @default.
• W2340891951 date "2017-03-06" @default.
• W2340891951 modified "2023-10-08" @default.
• W2340891951 title "Polynomial Splitting Measures and Cohomology of the Pure Braid Group" @default.
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• W2340891951 doi "https://doi.org/10.1007/s40598-017-0064-z" @default.
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