Tools

LEADER 03897cam a2200553 i 4500

001 ssj0003165350;

003 WaSeSS;

005 20260812090312.0;

006 m d ;

007 cr n ;

008 230415s2023 riua sb 000 0 eng d;

010 a| 2023012954;

020 a| 9781470456818q| (paperback);

020 z| 9781470474003q| (pdf);

035 a| (WaSeSS)ssj0003165350;

040 a| LBSORb| engc| LBSORd| WaSeSS;

042 a| pcc;

049 a| EREEa| NEHH;

050 00 a| QA387b| .G37 2023;

082 00 a| 512/.4822| 23/eng20230707;

084 a| 11F70a| 22E502| msc;

100 1 a| Gao, Fan,d| 1986-;

245 10 a| Local coefficients and gamma factors for principal series of covering groupsh| [electronic resource] /c| Fan Gao, Freydoon Shahidi, Dani Szpruch.;

260 a| Providence, RI :b| American Mathematical Society,c| 2023.;

300 a| v, 135 pages :b| illustrations ;c| 26 cm.;

490 0 a| Memoirs of the American Mathematical Society,x| 0065-9266 ;v| Volume 283, Number 1399.;

504 a| Includes bibliographical references (pages 131-135).;

505 0 a| Covering groups -- Local coefficients matrix and scattering matrix -- Plancherel measure and gamma factor -- Exceptional point and the Casselman-Shalika formula -- The fundamental group π1(Gv Q,n) and periodicity of bW,n -- Two Poincaré series -- Principal series of GL2 and SL -- Local coefficients matrix for SL -- Local coefficients matrices for GL2 and invariants via restrictions.;

506 a| Available only to authorized users.;

520 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 coefficients matrix, including the investigation of its arithmetic invariants. As a 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"--c| Provided by publisher.;

538 a| Mode of access: World Wide Web;

650 0 a| Automorphic forms.;

650 0 a| Topological groups.;

650 0 a| Local fields (Algebra);

650 0 a| Covering spaces (Topology);

650 7 a| Number theory -- Discontinuous groups and automorphic forms -- Representation-theoretic methods; automorphic representations over local and global fields.2| msc;

650 7 a| Topological groups, Lie groups -- Lie groups -- Representations of Lie and linear algebraic groups over local fields.2| msc;

655 0 a| Electronic books.;

700 1 a| Shahidi, Freydoon.;

700 1 a| Szpruch, Dani.;

856 40 z| Full text available from Ebook Central - Academic Completeu| https://ebookcentral.proquest.com/lib/eastcarolina/detail.action?docID=30494971;

949 a| CLICK ON WEB ADDRESSw| ASISh| JOYNER188;

949 a| CLICK ON WEB ADDRESSw| ASISh| HSL77;

949 a| CLICK ON WEB ADDRESSw| ASISh| JMUSIC60;

596 a| 1 3 4;

998 a| 6514687;

999 a| CLICK ON WEB ADDRESSw| ASISc| 1i| 6514687-1001l| JNETm| JOYNERr| Ys| Yt| JNESSBKu| 1/14/2025x| EBOOKz| JERESOURCE;

999 a| CLICK ON WEB ADDRESSw| ASISc| 1i| 6514687-2001l| HSLELECm| HSLr| Ys| Yt| HEBKu| 1/14/2025x| EBOOKz| HERESOURCE;

999 a| CLICK ON WEB ADDRESSw| ASISc| 1i| 6514687-3001l| MNETm| JMUSICr| Ys| Yt| MNESSBKu| 1/14/2025x| EBOOKz| JERESOURCE;

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

Author/creator	Gao, Fan, 1986-
Other author	Shahidi, Freydoon.
Other author	Szpruch, Dani.
Format	Electronic
Publication Info	Providence, RI : American Mathematical Society, 2023.
Description	v, 135 pages : illustrations ; 26 cm.
Supplemental Content	Full text available from Ebook Central - Academic Complete
Subjects	Automorphic forms. Topological groups. Local fields (Algebra) Covering spaces (Topology)

Series	Memoirs of the American Mathematical Society, 0065-9266 ; Volume 283, Number 1399.
Contents	Covering groups -- Local coefficients matrix and scattering matrix -- Plancherel measure and gamma factor -- Exceptional point and the Casselman-Shalika formula -- The fundamental group π1(Gv Q,n) and periodicity of bW,n -- Two Poincaré series -- Principal series of GL2 and SL -- Local coefficients matrix for SL -- Local coefficients matrices for GL2 and invariants via restrictions.
Abstract	"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 coefficients matrix, including the investigation of its arithmetic invariants. As a 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"-- Provided by publisher.
Bibliography note	Includes bibliographical references (pages 131-135).
Access restriction	Available only to authorized users.
Technical details	Mode of access: World Wide Web
Genre/form	Electronic books.
LCCN	2023012954
ISBN	9781470456818 (paperback)
ISBN	(pdf)

Availability

Library	Location	Call Number	Status	Item Actions
	Electronic Resources	Access Content Online	✔ Available

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

Click here for more information about this title

Availability