Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Jantzen coefficients and radical filtrations for generalized Verma
  modules   In this paper we give a sum formula for the radical filtration of generalized
Verma modules in any (possibly singular) blocks of parabolic BGG category which
can be viewed as a generalization of Jantzen sum formula for Verma modules in
the usual BGG category $\mathcal{O}$. Combined with Jantzen coefficients, we
determine the radical filtrations for all basic generalized Verma modules. The
proof makes use of the graded version of parabolic BGG category. Explicit
formulae for the graded decomposition numbers and inverse graded decomposition
numbers of generalized Verma modules in any (possibly singular) integral blocks
of the parabolic BGG category are also given.

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The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
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The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: patt-sol
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The categories of this paper are: mtrl-th
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The categories of this paper are: gr-qc
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The categories of this paper are: cs
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-ex
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-lat
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The categories of this paper are: physics
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-bio