scholarly journals Weil Representations of Symplectic Groups over Non-Principal Rings

2005 ◽  
Vol 35 (1) ◽  
pp. 309-329 ◽  
Author(s):  
Fernando Szechtman
Keyword(s):  
Symplectic Groups ◽  
Weil Representations

scholarly journals Clifford and Mackey theory for Weil representations of symplectic groups

2003 ◽  
Vol 262 (2) ◽  
pp. 348-379 ◽  
Author(s):  
Gerald Cliff ◽  
David McNeilly ◽  
Fernando Szechtman
Keyword(s):  
Symplectic Groups ◽  
Weil Representations

Weil Representations of Symplectic Groups Over Rings

2000 ◽  
Vol 62 (2) ◽  
pp. 423-436 ◽  
Author(s):  
Gerald Cliff ◽  
David McNeilly ◽  
Fernando Szechtman
Keyword(s):  
Symplectic Groups ◽  
Weil Representations

scholarly journals R-GROUP AND WHITTAKER SPACE OF SOME GENUINE REPRESENTATIONS

2021 ◽  
pp. 1-61
Author(s):  
Fan Gao
Keyword(s):  
Series Representation ◽  
Principal Series ◽  
Symplectic Groups ◽  
Principal Series Representation ◽  
Connected Group ◽  
Covering Group ◽  
Simply Connected

Abstract For a unitary unramified genuine principal series representation of a covering group, we study the associated R-group. We prove a formula relating the R-group to the dimension of the Whittaker space for the irreducible constituents of such a principal series representation. Moreover, for certain saturated covers of a semisimple simply connected group, we also propose a simpler conjectural formula for such dimensions. This latter conjectural formula is verified in several cases, including covers of the symplectic groups.

-ADIC -FUNCTIONS FOR ORDINARY FAMILIES ON SYMPLECTIC GROUPS

2019 ◽  
Vol 19 (4) ◽  
pp. 1287-1347 ◽  
Author(s):  
Zheng Liu
Keyword(s):  
Eisenstein Series ◽  
Symplectic Group ◽  
Symplectic Groups ◽  
Simple Strategy ◽  
Doubling Method

We construct the $p$-adic standard $L$-functions for ordinary families of Hecke eigensystems of the symplectic group $\operatorname{Sp}(2n)_{/\mathbb{Q}}$ using the doubling method. We explain a clear and simple strategy of choosing the local sections for the Siegel Eisenstein series on the doubling group $\operatorname{Sp}(4n)_{/\mathbb{Q}}$, which guarantees the nonvanishing of local zeta integrals and allows us to $p$-adically interpolate the restrictions of the Siegel Eisenstein series to $\operatorname{Sp}(2n)_{/\mathbb{Q}}\times \operatorname{Sp}(2n)_{/\mathbb{Q}}$.

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