Supercharacter formulas for pattern groups
TL;DR: In this article, a character formula for a supercharacter evaluated at a superclass for pattern groups and more generally for algebra groups is given, where the character is a set of characters which are constant on superclasses.
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Abstract: C. Andre and N. Yan introduced the idea of a supercharacter theory to give a tractable substitute for character theory in wild groups such as the unipotent uppertriangular group U n (F q ). In this theory superclasses are certain unions of conjugacy classes, and supercharacters are a set of characters which are constant on superclasses. This paper gives a character formula for a supercharacter evaluated at a superclass for pattern groups and more generally for algebra groups.
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Branching rules in the ring of superclass functions of unipotent upper-triangular matrices
TL;DR: The supercharacter theory of the finite group of unipotent upper-triangular matrices has a rich combinatorial structure built on set-partitions that is analogous to the partition combinatorics of the symmetric group as discussed by the authors.
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Superinduction for pattern groups
Eric Marberg,Nathaniel Thiem +1 more
TL;DR: In this article, it was shown that for two natural embeddings of U m in U n, super-induction is induction for U m and U n, and an explicit combinatorial algorithm for computing this induction analogous to the Pieri-formulas for the symmetric group was presented.
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Restricting supercharacters of the finite group of unipotent uppertriangular matrices
TL;DR: A Pieri-like restriction rule from $U_n$ to $U_{n-1}$ that can be described on set-partitions (analogous to the corresponding symmetric group rule on partitions) is described.
A supercharacter analogue for normality
TL;DR: In this article, the authors investigated the properties of algebra subgroups H⊂G which are unions of some set of the superclasses of G; they called such subgroups supernormal.
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References
•Book
Finite Groups of Lie Type: Conjugacy Classes and Complex Characters
Roger W. Carter
- 01 Aug 1993
TL;DR: The Steinberg Character as discussed by the authors is a character of Deligne-Lusztig, which is a generalization of the Steinberg character of Cuspidal Representations.
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