The Langlands-Shahidi L-Functions for Brylinski-Deligne Extensions
The Langlands-Shahidi L-Functions for Brylinski-Deligne Extensions
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Brylinski-Deligne 扩展的 Langlands-Shahidi L 函数
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通讯作者：
Fan Gao
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作者：
Fan Gao
We firstly discuss properties of the L-groups for Brylinski-Deligne extensions of split reductive groups constructed by M. Weissman. Secondly, the Gindikin-Karpelevich formula for an arbitrary Brylinski-Deligne extension is computed and expressed in terms of naturally defined elements of the group. Following this, we show that the Gindikin-Karpelevich formula can be interpreted as Langlands-Shahidi type L-functions associated with the adjoint action of the L-group for the Levi covering subgroup on certain Lie algebras. As a consequence, the constant term of Eisenstein series for Brylinski-Deligne extensions could be expressed in terms of global (partial) Langlands-Shahidi type L-functions. These L-functions are shown to possess meromorphic continuation to the whole complex plane. In the end, we determine the residual spectra of Brylinski-Deligne covers of some semisimple rank one groups.
