On character formulae for Weil representations for unitary groups over finite fields

2021 ◽  
pp. 1-11
Author(s):  
Takahiro Tsushima
Keyword(s):  
Finite Fields ◽  
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 Non-Hurwitz Classical Groups

2007 ◽  
Vol 10 ◽  
pp. 21-82 ◽  
Author(s):  
R. Vincent ◽  
A.E. Zalesski
Keyword(s):  
Finite Fields ◽  
Unitary Groups ◽  
Classical Groups ◽  
Special Linear ◽  
Low Dimensional

AbstractIn previous work by Di Martino, Tamburini and Zalesski [Comm. Algebra28 (2000) 5383–5404] it is shown that certain low-dimensional classical groups over finite fields are not Hurwitz. In this paper the list is extended by adding the special linear and special unitary groups in dimensions 8.9,11.13. We also show that all groups Sp(n, q) are not Hurwitz forqeven andn= 6,8,12,16. In the range 11 <n< 32 many of these groups are shown to be non-Hurwitz. In addition, we observe that PSp(6, 3),PΩ±(8, 3k),PΩ±10k), Ω(11,3k), Ω±(14,3k), Ω±(16,7k), Ω(n, 7k) forn= 9,11,13, PSp(8, 7k) are not Hurwitz.

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