Two conjectures on the Weil representations of finite symplectic and unitary groups

2020 ◽  
Vol 558 ◽  
pp. 485-490
Author(s):  
Gerhard Hiss ◽  
Moritz Schröer
Keyword(s):  
Unitary Groups ◽  
Weil Representations

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 Weil Representations of Unitary Groups

1999 ◽  
Vol 221 (1) ◽  
pp. 161-187 ◽  
Author(s):  
Fernando Szechtman
Keyword(s):  
Unitary Groups ◽  
Weil Representations

scholarly journals Vertical Distribution Relations for Special Cycles on Unitary Shimura Varieties

2018 ◽  
Vol 2020 (13) ◽  
pp. 3902-3926
Author(s):  
Réda Boumasmoud ◽  
Ernest Hunter Brooks ◽  
Dimitar P Jetchev
Keyword(s):  
Vertical Distribution ◽  
Three Dimensional ◽  
Complex Multiplication ◽  
Horizontal Distribution ◽  
Unitary Groups ◽  
Shimura Varieties ◽  
Heegner Points ◽  
Universal Norm

Abstract We consider cycles on three-dimensional Shimura varieties attached to unitary groups, defined over extensions of a complex multiplication (CM) field $E$, which appear in the context of the conjectures of Gan et al. [6]. We establish a vertical distribution relation for these cycles over an anticyclotomic extension of $E$, complementing the horizontal distribution relation of [8], and use this to define a family of norm-compatible cycles over these fields, thus obtaining a universal norm construction similar to the Heegner $\Lambda $-module constructed from Heegner points.

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