The value of the global intertwining operators on spherical vectors

Volker Heiermann

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The value of the global intertwining operators on spherical vectors

Volker Heiermann

Number Theory · Submitted 26 Sep 2017

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim Using Langlands-Shahidi theory, we compute the meromorphic function defined by the action of a global standard intertwining operator associated to chi on a spherical vector and show that the ratio of its poles in the positive Weyl chamber is well behaved.

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arXiv listing abstract v2. Results and the main claim are underlined; show every role.

Let F be a global field, G an unramified quasi-split reductive group over F and chi an everywhere unramified automorphic character of a maximal maximally split torus of G. Using Langlands-Shahidi theory, we compute the meromorphic function defined by the action of a global standard intertwining operator associated to chi on a spherical vector and show that the ratio of its poles in the positive Weyl chamber is well behaved.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	Let F be a global field, G an unramified quasi-split reductive group over F and chi an everywhere unramified automorphic character of a maximal maximally split torus of G.	background 1.00	0.07	0.02	unclear 0.57
s1	Using Langlands-Shahidi theory, we compute the meromorphic function defined by the action of a global standard intertwining operator associated to chi on a spherical vector and show that the ratio of its poles in the positive Weyl chamber is well behaved.	contribution 0.71	0.96	0.86	asserted 1.00

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Original abstract

Let F be a global field, G an unramified quasi-split reductive group over F and chi an everywhere unramified automorphic character of a maximal maximally split torus of G. Using Langlands-Shahidi theory, we compute the meromorphic function defined by the action of a global standard intertwining operator associated to chi on a spherical vector and show that the ratio of its poles in the positive Weyl chamber is well behaved.

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