Supercharacters of unipotent groups defined by involutions
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In this paper, the authors construct supercharacters of finite unipotent groups in the orthogonal, symplectic and unitary types, using group actions in a manner analogous to that of Diaconis and Isaacs.About:
This article is published in Journal of Algebra.The article was published on 2015-03-01 and is currently open access. It has received 33 citations till now. The article focuses on the topics: Unipotent & Unitary group.read more
Citations
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Supercharacter Theories Constructed by the Method of Little Groups
TL;DR: In this article, the authors modify the method of little groups to construct supercharacter theories of semidirect products with abelian normal subgroups, and apply this construction to reproduce known super character theories of several families of unipotent groups.
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Strong forms of linearization for Hopf monoids in species
TL;DR: In this article, it was shown that strongly linearized Hopf algebras have four bases, which one can view as analogs of the classical bases of the algebra of symmetric functions.
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The Hopf monoid on nonnesting supercharacters of pattern groups
TL;DR: In this paper, supercharacters and superclasses are constructed for a collection of unipotent matrix groups and a Hopf monoid is constructed from the super-characters.
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Supercharacter theories constructed by the method of little groups
TL;DR: The method of little groups as discussed by the authors describes the irreducible characters of semidirect products with abelian normal subgroups in terms of the IR characters of the factor groups.
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The Hopf monoid on nonnesting supercharacters of pattern groups
TL;DR: In this article, supercharacters and superclasses are constructed for a collection of unipotent matrix groups and a Hopf monoid is constructed from the superchar characters. But the supercharacter theory is not coarser than those defined by Diaconis-Isaacs for algebra groups and has superclasses indexed by nonnesting labeled set partitions.
References
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Supercharacters and superclasses for algebra groups
Persi Diaconis,I. M. Isaacs +1 more
TL;DR: In this paper, the supercharacters theory was extended to finite algebra groups, and the results of Andre and Yan were extended to the case of conjugacy classes in the upper triangular case.
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Basic characters of the unitriangular group (for arbitrary primes)
TL;DR: In this paper, it was shown that every irreducible (complex) character of U n (q) is a constituent of a unique basic character, which was proved under the assumption p > n, where p is the characteristic of the field F q with q elements.
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