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Restricting supercharacters of the finite group of unipotent uppertriangular matrices

Thiem, Nathaniel and Venkateswaran, Vidya (2009) Restricting supercharacters of the finite group of unipotent uppertriangular matrices. Electronic Journal of Combinatorics, 16 (1). R23. ISSN 1077-8926.

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It is well-known that understanding the representation theory of the finite group of unipotent upper-triangular matrices U_n over a finite field is a wild problem. By instead considering approximately irreducible representations (supercharacters), one obtains a rich combinatorial theory analogous to that of the symmetric group, where were place partition combinatorics with set-partitions. This paper studies the supercharacter theory of a family of subgroups that interpolate between Un-1 and Un. We supply several combinatorial indexing sets for the supercharacters, supercharacter formulas for these indexing sets, and a combinatorial rule for restricting supercharacters from one group to another. A consequence of this analysis is 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).

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Additional Information:© 2009 The Electronic Journal of Combinatorics. Aug 22, 2008; Accepted: Feb 9, 2009; Published: Feb 20, 2009. Part of this work is Venkateswaran's honors thesis at Stanford University. Mathematics Subject Classi�cation: 05E99, 20C33 The authors would like to thank Diaconis and Marberg for many enlightening discussions regarding this work, and anonymous referees for their comments.
Subject Keywords:05E99; 20C33
Issue or Number:1
Record Number:CaltechAUTHORS:20090410-153717314
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:13938
Deposited By: Tony Diaz
Deposited On:03 Aug 2009 22:53
Last Modified:03 Oct 2019 00:45

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