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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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| Auteur principal : | |
|---|---|
| Autres auteurs : | , |
| 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 : | |
| Documents associés : | Autre format:
Local coefficients and gamma factors for principal series of covering groups |
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| 200 | 1 | |a Local coefficients and gamma factors for principal series of covering groups |f Fan Gao, Freydoon Shahidi, Dani Szpruch | |
| 214 | 0 | |a Providence, RI |c AMS, American Mathematical Society |d 2023 | |
| 215 | |a 1 vol. (V-135 p.) |c illustrations |d 26 cm | ||
| 225 | 0 | |a Memoirs of the American Mathematical Society |x 0065-9266 |v 1399 | |
| 300 | |a "March 2023, volume 283, number 1399 (second of 7 numbers)" | ||
| 320 | |a Bibliogr. p. 131-135 | ||
| 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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