scholarly journals Weil representations and cusp forms on unitary groups

1974 ◽  
Vol 80 (6) ◽  
pp. 1137-1142 ◽  
Author(s):  
G. I. Lehrer
Keyword(s):  
Unitary Groups ◽  
Cusp Forms ◽  
Weil Representations

scholarly journals -ADIC EISENSTEIN SERIES AND -FUNCTIONS OF CERTAIN CUSP FORMS ON DEFINITE UNITARY GROUPS

2014 ◽  
Vol 15 (3) ◽  
pp. 471-510 ◽  
Author(s):  
Ellen Eischen ◽  
Xin Wan
Keyword(s):  
Positive Integer ◽  
Eisenstein Series ◽  
Constant Term ◽  
Unitary Groups ◽  
Cusp Forms ◽  
Imaginary Field

We construct$p$-adic families of Klingen–Eisenstein series and$L$-functions for cusp forms (not necessarily ordinary) unramified at an odd prime$p$on definite unitary groups of signature$(r,0)$(for any positive integer$r$) for a quadratic imaginary field${\mathcal{K}}$split at$p$. When$r=2$, we show that the constant term of the Klingen–Eisenstein family is divisible by a certain$p$-adic$L$-function.

scholarly journals LOCAL BORCHERDS PRODUCTS FOR UNITARY GROUPS

2017 ◽  
Vol 234 ◽  
pp. 139-169
Author(s):  
ERIC HOFMANN
Keyword(s):  
Boundary Component ◽  
Unitary Group ◽  
Picard Group ◽  
Unitary Groups ◽  
Weil Representation ◽  
Cusp Forms ◽  
Modular Variety ◽  
Arithmetic Subgroup ◽  
Torsion Element ◽  
Vector Valued

For the modular variety attached to an arithmetic subgroup of an indefinite unitary group of signature $(1,n+1)$, with $n\geqslant 1$, we study Heegner divisors in the local Picard group over a boundary component of a compactification. For this purpose, we introduce local Borcherds products. We obtain a precise criterion for local Heegner divisors to be torsion elements in the Picard group, and further, as an application, we show that the obstructions to a local Heegner divisor being a torsion element can be described by certain spaces of vector-valued elliptic cusp forms, transforming under a Weil representation.

scholarly journals Some Characterizations of the Weil Representations of the Symplectic and Unitary Groups

1997 ◽  
Vol 192 (1) ◽  
pp. 130-165 ◽  
Author(s):  
Pham Huu Tiep ◽  
Alexander E. Zalesskii
Keyword(s):  
Unitary Groups ◽  
Weil Representations

scholarly journals Clifford theory of Weil representations of unitary groups

2019 ◽  
Vol 22 (6) ◽  
pp. 975-999
Author(s):  
Moumita Shau ◽  
Fernando Szechtman
Keyword(s):  
Hermitian Form ◽  
Residue Field ◽  
Discrete Valuation Ring ◽  
Unitary Groups ◽  
Weil Representation ◽  
Congruence Subgroups ◽  
Weil Representations ◽  
Irreducible Components ◽  
Clifford Theory ◽  
Equivalence Type

Abstract Let {\mathcal{O}} be an involutive discrete valuation ring with residue field of characteristic not 2. Let A be a quotient of {\mathcal{O}} by a nonzero power of its maximal ideal, and let {*} be the involution that A inherits from {\mathcal{O}} . We consider various unitary groups {\mathcal{U}_{m}(A)} of rank m over A, depending on the nature of {*} and the equivalence type of the underlying hermitian or skew hermitian form. Each group {\mathcal{U}_{m}(A)} gives rise to a Weil representation. In this paper, we give a Clifford theory description of all irreducible components of the Weil representation of {\mathcal{U}_{m}(A)} with respect to all of its abelian congruence subgroups and a third of its nonabelian congruence subgroups.

scholarly journals Moments of Weil representations of finite special unitary groups

2020 ◽  
Vol 561 ◽  
pp. 237-255
Author(s):  
Nicholas M. Katz ◽  
Pham Huu Tiep
Keyword(s):  
Unitary Groups ◽  
Weil Representations

scholarly journals An Integral Representation of Standard AutomorphicLFunctions for Unitary Groups

2007 ◽  
Vol 2007 ◽  
pp. 1-22
Author(s):  
Yujun Qin
Keyword(s):  
Integral Representation ◽  
Eisenstein Series ◽  
Number Field ◽  
Unitary Group ◽  
Theta Series ◽  
Automorphic Representation ◽  
Unitary Groups ◽  
Cusp Forms ◽  
Cuspidal Automorphic Representation ◽  
Type Integral

LetFbe a number field,Ga quasi-split unitary group of rankn. We show that given an irreducible cuspidal automorphic representationπofG(A), its (partial)LfunctionLS(s,π,σ)can be represented by a Rankin-Selberg-type integral involving cusp forms ofπ, Eisenstein series, and theta series.

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