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- W2951101339 abstract "We generalize the character formulas for multiplicities of irreducible constituents from group theory to semigroup theory using Rota's theory of Mobius inversion. The technique works for a large class of semigroups including: inverse semigroups, semigroups with commuting idempotents, idempotent semigroups and semigroups with basic algebras. Using these tools we are able to give a complete description of the spectra of random walks on finite semigroups admitting a faithful representation by upper triangular matrices over the complex numbers. These include the random walks on chambers of hyperplane arrangements studied by Bidigare, Hanlon, Rockmere, Brown and Diaconis. Applications are also given to decomposing tensor powers and exterior products of rook matrix representations of inverse semigroups, generalizing and simplifying earlier results of Solomon for the rook monoid." @default.
- W2951101339 created "2019-06-27" @default.
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- W2951101339 date "2006-07-22" @default.
- W2951101339 modified "2023-09-27" @default.
- W2951101339 title "Mobius Functions and Semigroup Representation Theory II: Character formulas and multiplicities" @default.
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