scholarly journals On the local Langlands conjecture in prime dimension

1983 ◽  
Vol 9 (3) ◽  
pp. 323-326 ◽  
Author(s):  
Philip Kutzko ◽  
Allen Moy
Keyword(s):  
Local Langlands Conjecture ◽  
Prime Dimension

scholarly journals On the Local Langlands Conjecture in Prime Dimension

1985 ◽  
Vol 121 (3) ◽  
pp. 495 ◽  
Author(s):  
Philip Kutzko ◽  
Allen Moy
Keyword(s):  
Local Langlands Conjecture ◽  
Prime Dimension

scholarly journals The intersection graph of a finite simple group has diameter at most 5

2021 ◽  
Author(s):  
Saul D. Freedman
Keyword(s):  
Simple Group ◽  
Upper Bound ◽  
Finite Simple Group ◽  
Unitary Groups ◽  
Intersection Graph ◽  
Monster Group ◽  
Prime Dimension

AbstractLet G be a non-abelian finite simple group. In addition, let $$\Delta _G$$ Δ G be the intersection graph of G, whose vertices are the proper non-trivial subgroups of G, with distinct subgroups joined by an edge if and only if they intersect non-trivially. We prove that the diameter of $$\Delta _G$$ Δ G has a tight upper bound of 5, thereby resolving a question posed by Shen (Czechoslov Math J 60(4):945–950, 2010). Furthermore, a diameter of 5 is achieved only by the baby monster group and certain unitary groups of odd prime dimension.

scholarly journals Cycles in the de Rham cohomology of abelian varieties over number fields

2018 ◽  
Vol 154 (4) ◽  
pp. 850-882
Author(s):  
Yunqing Tang
Keyword(s):  
Endomorphism Ring ◽  
Abelian Varieties ◽  
Number Fields ◽  
De Rham Cohomology ◽  
Tate Conjecture ◽  
De Rham ◽  
Prime Dimension

In his 1982 paper, Ogus defined a class of cycles in the de Rham cohomology of smooth proper varieties over number fields. This notion is a crystalline analogue of$\ell$-adic Tate cycles. In the case of abelian varieties, this class includes all the Hodge cycles by the work of Deligne, Ogus, and Blasius. Ogus predicted that such cycles coincide with Hodge cycles for abelian varieties. In this paper, we confirm Ogus’ prediction for some families of abelian varieties. These families include geometrically simple abelian varieties of prime dimension that have non-trivial endomorphism ring. The proof uses a crystalline analogue of Faltings’ isogeny theorem due to Bost and the known cases of the Mumford–Tate conjecture.

On the local Langlands conjecture forGL(2)

1978 ◽  
Vol 46 (2) ◽  
pp. 179-200 ◽  
Author(s):  
Jerrold B. Tunnell
Keyword(s):  
Local Langlands Conjecture

scholarly journals Mutually unbiased unitary bases of operators on d-dimensional hilbert space

2020 ◽  
Vol 18 (01) ◽  
pp. 1941026 ◽  
Author(s):  
Rinie N. M. Nasir ◽  
Jesni Shamsul Shaari ◽  
Stefano Mancini
Keyword(s):  
Hilbert Space ◽  
Hilbert Spaces ◽  
Unitary Operator ◽  
Dimensional Subspace ◽  
Mutually Unbiased Bases ◽  
Unitary Operators ◽  
Dimension Formula ◽  
Dimensional Hilbert Space ◽  
Prime Dimension

Analogous to the notion of mutually unbiased bases for Hilbert spaces, we consider mutually unbiased unitary bases (MUUBs) for the space of operators, [Formula: see text], acting on such Hilbert spaces. The notion of MUUB reflects the equiprobable guesses of unitary operators in one basis of [Formula: see text] when estimating a unitary operator in another. Though, for prime dimension [Formula: see text], the maximal number of MUUBs is known to be [Formula: see text], there is no known recipe for constructing them, assuming they exist. However, one can always construct a minimum of three MUUBs, and the maximal number is approached for very large values of [Formula: see text]. MUUBs can also exist for some [Formula: see text]-dimensional subspace of [Formula: see text] with the maximal number being [Formula: see text].

Simultaneous equidistributing and non-dense points for non-commuting toral automorphisms

2018 ◽  
Vol 40 (1) ◽  
pp. 175-193
Author(s):  
MANFRED EINSIEDLER ◽  
ALEX MAIER
Keyword(s):  
Hausdorff Dimension ◽  
Dense Orbit ◽  
Set Of Points ◽  
Toral Automorphisms ◽  
Prime Dimension

We show in prime dimension that for two non-commuting totally irreducible toral automorphisms the set of points that equidistribute under the first map but have non-dense orbit under the second has full Hausdorff dimension. In non-prime dimension the argument fails only if the automorphisms have strong algebraic relations.

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