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{\bf Nathaniel Thiem and Vidya Venkateswaran}
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{\bf Restricting Supercharacters of the Finite Group of Unipotent Uppertriangular Matrices}
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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
we replace partition combinatorics with set-partitions.  This paper
studies the supercharacter theory of a family of subgroups that
interpolate between $U_{n-1}$ and $U_n$.  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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