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- W2023482777 abstract "By algebraic group theory, there is a map from the semisimple conjugacy classes of a finite group of Lie type to the conjugacy classes of the Weyl group. Picking a semisimple class uniformly at random yields a probability measure on conjugacy classes of the Weyl group. Using the Brauer complex, it is proved that this measure agrees with a second measure on conjugacy classes of the Weyl group induced by a construction of Cellini using the affine Weyl group. Formulas for Cellini's measure in type A are found. This leads to new models of card shuffling and has interesting combinatorial and number-theoretic consequences. An analysis of type C gives another solution to a problem of Rogers in dynamical systems: the enumeration of unimodal permutations by cycle structure. The proof uses the factorization theory of palindromic polynomials over finite fields. Contact is made with symmetric function theory." @default.
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- W2023482777 date "2001-09-01" @default.
- W2023482777 modified "2023-09-30" @default.
- W2023482777 title "Applications of the Brauer Complex: Card Shuffling, Permutation Statistics, and Dynamical Systems" @default.
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- W2023482777 doi "https://doi.org/10.1006/jabr.2001.8814" @default.
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