Restrictions of rainbow supercharacters
نویسندگان
چکیده
منابع مشابه
Restrictions of Rainbow Supercharacters and Poset Binomials
A supercharacter theory of a finite group is a natural approximation to the ordinary character theory. There is a particularly nice supercharacter theory for Un, the group of unipotent upper triangular matrices over a finite field, that has a rich combinatorial structure based on set partitions. Various representation theoretic constructions such as restriction and induction have supercharacter...
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This paper introduces a variation on the binomial coefficient that depends on a poset and interpolates between q-binomials and 1-binomials: a total order gives the usual q-binomial, and a poset with no relations gives the usual binomial coefficient. These coefficients arise naturally in the study of supercharacters of the finite groups of unipotent upper-triangular matrices, whose representatio...
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The standard supercharacter theory of the finite unipotent upper-triangular matrices Un(q) gives rise to a beautiful combinatorics based on set partitions. As with the representation theory of the symmetric group, embeddings of Um(q) ⊆ Un(q) for m ≤ n lead to branching rules. Diaconis and Isaacs established that the restriction of a supercharacter of Un(q) is a nonnegative integer linear combin...
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The standard supercharacter theory of the finite unipotent upper-triangular matrices Un(q) gives rise to a beautiful combinatorics based on set partitions. As with the representation theory of the symmetric group, embeddings of Um(q) ⊆ Un(q) for m ≤ n lead to branching rules. Diaconis and Isaacs established that the restriction of a supercharacter of Un(q) is a nonnegative integer linear combin...
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Before the workshop, we suggested that the following reading list [1, 2, 3, 4, 5, 6] would be a good refreshment for all of us. At the start of the workshop, we identified the following problems that were worth considering given the recent progress in the area. 1. Higman’s conjecture. 2. Compute the antipode of the monoid scf(U) in the supercharacter basis. 3. Explicitly describe the multiplica...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2016
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2015.11.037