Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nonzero coefficients in restrictions and tensor products of
  supercharacters of $U_n(q)$   The standard supercharacter theory of the finite unipotent upper-triangular
matrices $U_n(q)$ gives rise to a beautiful combinatorics based on set
partitions. As with the representation theory of the symmetric group,
embeddings of $U_m(q)\subseteq U_n(q)$ for $m\leq n$ lead to branching rules.
Diaconis and Isaacs established that the restriction of a supercharacter of
$U_n(q)$ is a nonnegative integer linear combination of supercharacters of
$U_m(q)$ (in fact, it is polynomial in $q$). In a first step towards
understanding the combinatorics of coefficients in the branching rules of the
supercharacters of $U_n(q)$, this paper characterizes when a given coefficient
is nonzero in the restriction of a supercharacter and the tensor product of two
supercharacters. These conditions are given uniformly in terms of complete
matchings in bipartite graphs.

4
The categories of this paper are: cond-mat
28
The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph
9
The categories of this paper are: nlin
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The categories of this paper are: q-fin
8
The categories of this paper are: hep-ex
12
The categories of this paper are: nucl-th
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The categories of this paper are: eess
30
The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
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The categories of this paper are: dg-ga
36
The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci