Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Category $\mathcal{O}$ over triangular Generalized Weyl Algebras   We analyze the BGG Category $\mathcal{O}$ over a large class of generalized
Weyl algebras (henceforth termed GWAs). Given such a "triangular" GWA for which
Category $\mathcal{O}$ decomposes into a direct sum of subcategories, we study
in detail the homological properties of blocks with finitely many simples. As
consequences, we show that the endomorphism algebra of a projective generator
of such a block is quasi-hereditary, finite-dimensional, and graded Koszul. We
also classify all tilting modules in the block, as well as all submodules of
all projective and tilting modules. Finally, we present a novel connection
between blocks of triangular GWAs and Young tableaux, which provides a
combinatorial interpretation of morphisms and extensions between objects of the
block.

29
The categories of this paper are: funct-an
18
The categories of this paper are: econ
30
The categories of this paper are: q-alg
17
The categories of this paper are: q-fin
1
The categories of this paper are: cs
34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph
22
The categories of this paper are: chao-dyn
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The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
24
The categories of this paper are: dg-ga