Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Casselman-Shahidi's conjecture on normalized intertwining operators for
  groups of classical type   Intertwining operators play an essential role and appear everywhere in the
Langlands program, their analytic properties interact directly, yet deeply with
the decomposition of parabolic induction locally and the residues of Eisenstein
series globally. Inspired by the profound Langlands-Shahidi theory,
Casselman-Shahidi conjectured that a certain normalization factor would govern
the singularity of intertwining operators for generic standard modules. Indeed,
motivated by the theory of theta correspondence, especially the Siegel-Weil
formula globally, and the composition problem of degenerate principal series
and the demand of a g.c.d. definition of standard $L$-functions in the
framework of the doubling method locally, an optimal normalization factor has
been determined for degenerate principal series of classical groups via the
theory of integrals on prehomogeneous vector spaces. Such a method seems
impossible to be generalized to work even in the setting of degenerate
generalized principal series, which are naturally involved in the recent
Cai-Friedberg-Ginzburg-Kaplan's generalized doubling method. To circumvent it,
we discover a new uniform argument that can answer the singularity problem of
intertwining operators for a large class of induced representations. As an
illustration, we prove the aforementioned Casselman-Shahidi conjecture for
quasi-split groups of classical type in the paper. Along the way, with the help
of Shahidi's local coefficient theory, we also prove that those normalized
intertwining operators are always non-zero, and provide a new one-sentence
proof of the standard module conjecture in the spirit of Casselman-Shahidi.

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The categories of this paper are: chem-ph
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The categories of this paper are: eess
13
The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
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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: nucl-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: solv-int
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The categories of this paper are: stat
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The categories of this paper are: q-fin
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The categories of this paper are: math-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: atom-ph
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The categories of this paper are: adap-org