Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Shell Tableaux: A set partition analogue of vacillating tableaux   Schur-Weyl duality is a fundamental framework in combinatorial representation
theory. It intimately relates the irreducible representations of a group to the
irreducible representations of its centralizer algebra. We investigate the
analog of Schur-Weyl duality for the group of unipotent upper triangular
matrices over a finite field. In this case, the character theory of these upper
triangular matrices is "wild" or unattainable. Thus we employ a generalization,
known as supercharacter theory, that creates a striking variation on the
character theory of the symmetric group with combinatorics built from set
partitions. In this paper, we present a combinatorial formula for calculating a
restriction and induction of supercharacters based on statistics of set
partitions and seashell inspired diagrams. We use these formulas to create a
graph that encodes the decomposition of a tensor space, and develop an analog
of Young tableaux, known as shell tableaux, to index paths in this graph.

36
The categories of this paper are: cmp-lg
5
The categories of this paper are: gr-qc
22
The categories of this paper are: chao-dyn
6
The categories of this paper are: astro-ph
0
The categories of this paper are: hep-ph
11
The categories of this paper are: hep-lat
18
The categories of this paper are: econ
1
The categories of this paper are: cs
28
The categories of this paper are: alg-geom
27
The categories of this paper are: comp-gas
21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
15
The categories of this paper are: nucl-ex
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
7
The categories of this paper are: hep-th