LAUSR

Plancherel formula for $${{\,\mathrm{\mathrm {GL}}\,}}_n(F){\backslash } {{\,\mathrm{\mathrm {GL}}\,}}_n(E)$$ and applications to the Ichino–Ikeda and formal degree conjectures for unitary groups

Sign Up to like & get
recommendations!
1 Published in 2021 at "Inventiones Mathematicae"

DOI: 10.1007/s00222-021-01032-6

Abstract: We establish an explicit Plancherel decomposition for $${{\,\mathrm{\mathrm {GL}}\,}}_n(F){\backslash } {{\,\mathrm{\mathrm {GL}}\,}}_n(E)$$ where E/F is a quadratic extension of local fields of characteristic zero by making use of a local functional equation for Asai $$\gamma… read more here.

Keywords: mathrm mathrm; mathrm; mathrm backslash; ichino ikeda ... See more keywords

OD-Characterization of Some Simple Unitary Groups

Sign Up to like & get
recommendations!
0 Published in 2018 at "Bulletin of the Iranian Mathematical Society"

DOI: 10.1007/s41980-020-00376-8

Abstract: We show that the simple unitary groups $$U_3(q)$$ U 3 ( q ) and $$U_4(q)$$ U 4 ( q ) , with $$2< q < 10^2$$ 2 < q < 10 2 a prime power,… read more here.

Keywords: unitary groups; characterization simple; simple unitary;

Theta lifting for tempered representations of real unitary groups

Sign Up to like & get
recommendations!
1 Published in 2022 at "Advances in Mathematics"

DOI: 10.1016/j.aim.2022.108188

Abstract: We study the theta lifting for real unitary groups and completely determine the theta lifts of tempered representations. In particular, we show that the theta lifts of (limits of) discrete series representations can be expressed… read more here.

Keywords: unitary groups; tempered representations; theta lifting; representations real ... See more keywords

Moments of Weil representations of finite special unitary groups

Sign Up to like & get
recommendations!
1 Published in 2020 at "Journal of Algebra"

DOI: 10.1016/j.jalgebra.2019.02.039

Abstract: Abstract We prove an “nth moment =1” result for irreducible Weil representations of degree ( q n + 1 ) / ( q + 1 ) of special unitary groups SU n ( q )… read more here.

Keywords: moments weil; special unitary; unitary groups; finite special ... See more keywords

On presentations for unitary groups

Sign Up to like & get
recommendations!
1 Published in 2020 at "Journal of Algebra"

DOI: 10.1016/j.jalgebra.2019.02.043

Abstract: Abstract Concise presentations for groups are useful for both theoretical and computational purposes. We give short 2-generator presentations for the 3-dimensional unitary groups U 3 ( q ) and S U 3 ( q )… read more here.

Keywords: unitary groups; presentations unitary;

2-Minimal subgroups of monomial, linear and unitary groups

Sign Up to like & get
recommendations!
0 Published in 2020 at "Journal of Algebra"

DOI: 10.1016/j.jalgebra.2019.10.003

Abstract: Abstract This paper gives a detailed and explicit description of all the 2-minimal subgroups for the finite linear and unitary groups defined over fields of odd characteristic. Also the 2-minimal subgroups of all the subgroups… read more here.

Keywords: monomial linear; minimal subgroups; unitary groups; linear unitary ... See more keywords

The E-normal structure of odd dimensional unitary groups

Sign Up to like & get
recommendations!
1 Published in 2018 at "Journal of Pure and Applied Algebra"

DOI: 10.1016/j.jpaa.2017.11.002

Abstract: In this paper we define odd dimensional unitary groups $U_{2n+1}(R,\Delta)$. These groups contain as special cases the odd dimensional general linear groups $GL_{2n+1}(R)$ where $R$ is any ring, the odd dimensional orthogonal and symplectic groups… read more here.

Keywords: structure odd; dimensional unitary; unitary groups; normal structure ... See more keywords

The essential 2-rank of general linear and unitary groups

Sign Up to like & get
recommendations!
1 Published in 2021 at "Journal of Pure and Applied Algebra"

DOI: 10.1016/j.jpaa.2020.106518

Abstract: Abstract Let G be a general linear or unitary group over a finite field of odd characteristic and let D ≤ G be a Sylow 2-subgroup. In this paper, we classify essential subgroups of the… read more here.

Keywords: essential rank; unitary groups; general linear; linear unitary ... See more keywords

The E-normal structure of Petrov’s odd unitary groups over commutative rings

Sign Up to like & get
recommendations!
1 Published in 2019 at "Communications in Algebra"

DOI: 10.1080/00927872.2019.1677689

Abstract: Abstract For an odd quadratic space of Witt index over a commutative ring with pseudoinvolution, we classify the subgroups of the odd unitary group that are normalized by the elementary subgroup defined by a hyperbolic… read more here.

Keywords: normal structure; unitary groups; petrov odd; odd unitary ... See more keywords

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

Sign Up to like & get
recommendations!
1 Published in 2021 at "Communications in Algebra"

DOI: 10.1080/00927872.2021.1926472

Abstract: Abstract We calculate characters of Weil representations of unitary groups over finite fields geometrically. As a byproduct, we deduce another proof of Gérardin’s trace formula for the Weil representation. Our main ingredient is an explicit… read more here.

Keywords: weil representations; representations unitary; finite fields; unitary groups ... See more keywords

Clifford theory of Weil representations of unitary groups

Sign Up to like & get
recommendations!
0 Published in 2019 at "Journal of Group Theory"

DOI: 10.1515/jgth-2018-0151

Abstract: Abstract Let 𝒪{\mathcal{O}} be an involutive discrete valuation ring with residue field of characteristic not 2. Let A be a quotient of 𝒪{\mathcal{O}} by a nonzero power of its maximal ideal, and let *{*} be… read more here.

Keywords: clifford theory; theory; unitary groups; representations unitary ... See more keywords