Local coefficients and gamma factors for principal series of covering groups

Local coefficients and gamma factors for principal series of covering groups

We consider an n-fold Brylinski-Deligne cover of a reductive group over a p-adic field. Since the space of Whittaker functionals of an irreducible genuine representation of such a cover is not one-dimensional, one can consider a local coefficients matrix arising from an intertwining operator, which...

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Détails bibliographiques
Auteur principal : Gao Fan (Auteur)
Autres auteurs : Shahidi Freydoon (Auteur), Szpruch Dani (Auteur)
Format : Livre
Langue : anglais
Titre complet : Local coefficients and gamma factors for principal series of covering groups / Fan Gao, Freydoon Shahidi, Dani Szpruch
Publié : Providence, RI : AMS, American Mathematical Society , 2023
Description matérielle : 1 vol. (V-135 p.)
Collection : Memoirs of the American Mathematical Society ; 1399
Sujets :
Théorie des nombres
Documents associés : Autre format: Local coefficients and gamma factors for principal series of covering groups
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330 |a We consider an n-fold Brylinski-Deligne cover of a reductive group over a p-adic field. Since the space of Whittaker functionals of an irreducible genuine representation of such a cover is not one-dimensional, one can consider a local coefficients matrix arising from an intertwining operator, which is the natural analogue of the local coefficients in the linear case. In this paper, we concentrate on genuine principal series representations and establish some fundamental properties of such a local consequence, we prove a form of the Casselman-Shalika formula which could be viewed as a natural analogue for linear algebraic groups. We also investigate in some depth the behaviour of the local coefficients matrix with respect to the restriction of genuine principal series from covers of GL to SL . In particular, some further relations are unveiled between local coefficients matrices and gamma factors or metaplectic-gamma factors--Abstract, pg. v 
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