Local coefficients and gamma factors for principal series of covering groups / Fan Gao, Freydoon Shahidi, Dani Szpruch.

Format:

Book

Author/Creator:

Gao, Fan, 1986- author.

Shahidi, Freydoon, author.

Szpruch, Dani, author.

Series:

Memoirs of the American Mathematical Society ; no. 1399.

Memoirs of the American Mathematical Society, 0065-9266 ; number 1399

Language:

English

Subjects (All):

Mathematical physics.

Physical Description:

v, 135 pages : illustrations ; 26 cm.

Place of Publication:

Providence, RI : AMS, American Mathematical Society, 2023.

Summary:

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 GL₂ to SL₂. In particular, some further relations are unveiled between local coefficients matrices and gamma factors or metaplectic-gamma factors--Abstract, pg. v.

Notes:

"March 2023, volume 283, number 1399 (second of 7 numbers)"

Includes bibliographical references (pages 131-135).

ISBN:

9781470456818

1470456818

OCLC:

1372297750