scholarly journals Weil representations of unitary groups over ramified extensions of finite local rings with odd nilpotency length

2019 ◽  
Vol 47 (8) ◽  
pp. 3007-3024
Author(s):  
Fernando Szechtman ◽  
Momuita Shau ◽  
Allen Herman
Keyword(s):  
Unitary Groups ◽  
Local Rings ◽  
Weil Representations

scholarly journals Unitary groups over local rings

1978 ◽  
Vol 52 (2) ◽  
pp. 354-363 ◽  
Author(s):  
D.G. James
Keyword(s):  
Unitary Groups ◽  
Local Rings

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 UNITARY GROUPS OVER LOCAL RINGS

2013 ◽  
Vol 13 (02) ◽  
pp. 1350093 ◽  
Author(s):  
J. CRUICKSHANK ◽  
A. HERMAN ◽  
R. QUINLAN ◽  
F. SZECHTMAN
Keyword(s):  
Local Ring ◽  
Unitary Group ◽  
Quadratic Extension ◽  
Unitary Groups ◽  
Weil Representation ◽  
Local Rings ◽  
Hermitian Forms ◽  
Finite Local Ring

We study hermitian forms and unitary groups defined over a local ring, not necessarily commutative, equipped with an involution. When the ring is finite we obtain formulae for the order of the unitary groups as well as their point stabilizers, and use these to compute the degrees of the irreducible constituents of the Weil representation of a unitary group associated to a ramified quadratic extension of a finite local ring.

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
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