Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lattice structure of Weyl groups via representation theory of
  preprojective algebras   This paper studies the combinatorics of lattice congruences of the weak order
on a finite Weyl group $W$, using representation theory of the corresponding
preprojective algebra $\Pi$. Natural bijections are constructed between
important objects including join-irreducible congruences, join-irreducible
(respectively, meet-irreducible) elements of $W$, indecomposable $\tau$-rigid
(respectively, $\tau^-$-rigid) modules and layers of $\Pi$. The
lattice-theoretically natural labeling of the Hasse quiver by join-irreducible
elements of $W$ is shown to coincide with the algebraically natural labelling
by layers of $\Pi$. We show that layers of $\Pi$ are nothing but bricks (or
equivalently stones, or 2-spherical modules). The forcing order on
join-irreducible elements of $W$ (arising from the study of lattice
congruences) is described algebraically in terms of the doubleton extension
order. We give a combinatorial description of indecomposable $\tau^-$-rigid
modules for type $A$ and $D$.

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The categories of this paper are: hep-th
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
20
The categories of this paper are: acc-phys
9
The categories of this paper are: nlin
1
The categories of this paper are: cs
15
The categories of this paper are: nucl-ex
5
The categories of this paper are: gr-qc
18
The categories of this paper are: econ
12
The categories of this paper are: nucl-th
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
8
The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph
23
The categories of this paper are: solv-int
30
The categories of this paper are: q-alg