Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Determinantal modules over preprojective algebras and representations of
  Dynkin quivers   In this paper, we study extension groups of modules over a preprojective
algebra via the Auslander-Reiten translation of the quiver associated with it.
More precisely, based on the recent work given by Aizenbud and Lapid, we give a
description of extension groups of a preprojective algebra in terms of the AR
translation and nilpotent matrices. As a result, we calculate the extension
group of a sort of so-called determinantal modules, which is an analog of
quantum minors in quantum coordinate rings. In particular, we give an
equivalent combinatorial condition when the product of two quantum minors (up
to $q$-power rescaling) belongs to the dual canonical basis of quantum
coordinate rings in the Dynkin case.

0
The categories of this paper are: hep-ph
11
The categories of this paper are: hep-lat
26
The categories of this paper are: bayes-an
25
The categories of this paper are: patt-sol
20
The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas
19
The categories of this paper are: eess
12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
4
The categories of this paper are: cond-mat
32
The categories of this paper are: atom-ph
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
17
The categories of this paper are: q-fin
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom