Displaying similar documents to “Compatibility of the theta correspondence with the Whittaker functors”

Geometric theta-lifting for the dual pair 𝕊𝕆 2 m , 𝕊 p 2 n

Sergey Lysenko (2011)

Annales scientifiques de l'École Normale Supérieure

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Let X be a smooth projective curve over an algebraically closed field of characteristic  > 2 . Consider the dual pair H = SO 2 m , G = Sp 2 n over X with H split. Write Bun G and Bun H for the stacks of G -torsors and H -torsors on X . The theta-kernel Aut G , H on Bun G × Bun H yields theta-lifting functors F G : D ( Bun H ) D ( Bun G ) and F H : D ( Bun G ) D ( Bun H ) between the corresponding derived categories. We describe the relation of these functors with Hecke operators. In two particular cases these functors realize the geometric Langlands functoriality for the above pair (in the non...

The Massera-Schäffer problem for a first order linear differential equation

Nina A. Chernyavskaya, Leonid A. Shuster (2022)

Czechoslovak Mathematical Journal

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We consider the Massera-Schäffer problem for the equation - y ' ( x ) + q ( x ) y ( x ) = f ( x ) , x , where f L p loc ( ) , p [ 1 , ) and 0 q L 1 loc ( ) . By a solution of the problem we mean any function y , absolutely continuous and satisfying the above equation almost everywhere in . Let positive and continuous functions μ ( x ) and θ ( x ) for x be given. Let us introduce the spaces L p ( , μ ) = f L p loc ( ) : f L p ( , μ ) p = - | μ ( x ) f ( x ) | p d x < , L p ( , θ ) = f L p loc ( ) : f L p ( , θ ) p = - | θ ( x ) f ( x ) | p d x < . We obtain requirements to the functions μ , θ and q under which (1) for every function f L p ( , θ ) there exists a unique solution y L p ( , μ ) of the above equation; (2) there is an absolute constant...

The general rigidity result for bundles of A -covelocities and A -jets

Jiří M. Tomáš (2017)

Czechoslovak Mathematical Journal

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Let M be an m -dimensional manifold and A = 𝔻 k r / I = N A a Weil algebra of height r . We prove that any A -covelocity T x A f T x A * M , x M is determined by its values over arbitrary max { width A , m } regular and under the first jet projection linearly independent elements of T x A M . Further, we prove the rigidity of the so-called universally reparametrizable Weil algebras. Applying essentially those partial results we give the proof of the general rigidity result T A * M T r * M without coordinate computations, which improves and generalizes the partial...

Factorizations of normality via generalizations of β -normality

Ananga Kumar Das, Pratibha Bhat, Ria Gupta (2016)

Mathematica Bohemica

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The notion of β -normality was introduced and studied by Arhangel’skii, Ludwig in 2001. Recently, almost β -normal spaces, which is a simultaneous generalization of β -normal and almost normal spaces, were introduced by Das, Bhat and Tartir. We introduce a new generalization of normality, namely weak β -normality, in terms of θ -closed sets, which turns out to be a simultaneous generalization of β -normality and θ -normality. A space X is said to be weakly β -normal (w β -normal ) if for every...

Singularities of 2 Θ -divisors in the jacobian

Christian Pauly, Emma Previato (2001)

Bulletin de la Société Mathématique de France

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We consider the linear system | 2 Θ 0 | of second order theta functions over the Jacobian J C of a non-hyperelliptic curve C . A result by J.Fay says that a divisor D | 2 Θ 0 | contains the origin 𝒪 J C with multiplicity 4 if and only if D contains the surface C - C = { 𝒪 ( p - q ) p , q C } J C . In this paper we generalize Fay’s result and some previous work by R.C.Gunning. More precisely, we describe the relationship between divisors containing 𝒪 with multiplicity 6 , divisors containing the fourfold C 2 - C 2 = { 𝒪 ( p + q - r - s ) p , q , r , s C } , and divisors singular along C - C , using...

On almost complex structures from classical linear connections

Jan Kurek, Włodzimierz M. Mikulski (2017)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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Let f m be the category of m -dimensional manifolds and local diffeomorphisms and  let T be the tangent functor on f m . Let 𝒱 be the category of real vector spaces and linear maps and let 𝒱 m be the category of m -dimensional real vector spaces and linear isomorphisms. We characterize all regular covariant functors F : 𝒱 m 𝒱 admitting f m -natural operators J ˜ transforming classical linear connections on m -dimensional manifolds M into almost complex structures J ˜ ( ) on F ( T ) M = x M F ( T x M ) .

Cotorsion pairs in comma categories

Yuan Yuan, Jian He, Dejun Wu (2024)

Czechoslovak Mathematical Journal

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Let 𝒜 and be abelian categories with enough projective and injective objects, and T : 𝒜 a left exact additive functor. Then one has a comma category ( T ) . It is shown that if T : 𝒜 is 𝒳 -exact, then ( 𝒳 , 𝒳 ) is a (hereditary) cotorsion pair in 𝒜 and ( 𝒴 , 𝒴 ) ) is a (hereditary) cotorsion pair in if and only if 𝒳 𝒴 , 𝐡 ( 𝒳 , 𝒴 ) ) is a (hereditary) cotorsion pair in ( T ) and 𝒳 and 𝒴 are closed under extensions. Furthermore, we characterize when special preenveloping classes in abelian categories 𝒜 and can induce special preenveloping...

A new characterization for the simple group PSL ( 2 , p 2 ) by order and some character degrees

Behrooz Khosravi, Behnam Khosravi, Bahman Khosravi, Zahra Momen (2015)

Czechoslovak Mathematical Journal

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Let G be a finite group and p a prime number. We prove that if G is a finite group of order | PSL ( 2 , p 2 ) | such that G has an irreducible character of degree p 2 and we know that G has no irreducible character θ such that 2 p θ ( 1 ) , then G is isomorphic to PSL ( 2 , p 2 ) . As a consequence of our result we prove that PSL ( 2 , p 2 ) is uniquely determined by the structure of its complex group algebra.

The CR Yamabe conjecture the case n = 1

Najoua Gamara (2001)

Journal of the European Mathematical Society

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Let ( M , θ ) be a compact CR manifold of dimension 2 n + 1 with a contact form θ , and L = ( 2 + 2 / n ) Δ b + R its associated CR conformal laplacien. The CR Yamabe conjecture states that there is a contact form θ ˜ on M conformal to θ which has a constant Webster curvature. This problem is equivalent to the existence of a function u such that L u = u 1 + 2 / n , u > 0 on M . D. Jerison and J. M. Lee solved the CR Yamabe problem in the case where n 2 and ( M , θ ) is not locally CR equivalent to the sphere S 2 n + 1 of 𝐂 n . In a join work with R. Yacoub, the CR Yamabe...

Stable tubes in extriangulated categories

Li Wang, Jiaqun Wei, Haicheng Zhang (2022)

Czechoslovak Mathematical Journal

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Let 𝒳 be a semibrick in an extriangulated category. If 𝒳 is a τ -semibrick, then the Auslander-Reiten quiver Γ ( ( 𝒳 ) ) of the filtration subcategory ( 𝒳 ) generated by 𝒳 is 𝔸 . If 𝒳 = { X i } i = 1 t is a τ -cycle semibrick, then Γ ( ( 𝒳 ) ) is 𝔸 / τ 𝔸 t .

Limits and colimits in certain categories of spaces of continuous functions

Marvin W. Grossman

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CONTENTSIntroduction................................................................................................................................................................................5§ 1. Notation and preliminaries.............................................................................................................................................6§ 2. Epimorphisms and monomorphisms.........................................................................................................................7§...

On the cardinality of Urysohn spaces and weakly H -closed spaces

Fortunata Aurora Basile, Nathan Carlson (2019)

Mathematica Bohemica

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We introduce the cardinal invariant θ - a L ' ( X ) , related to θ - a L ( X ) , and show that if X is Urysohn, then | X | 2 θ - a L ' ( X ) χ ( X ) . As θ - a L ' ( X ) a L ( X ) , this represents an improvement of the Bella-Cammaroto inequality. We also introduce the classes of firmly Urysohn spaces, related to Urysohn spaces, strongly semiregular spaces, related to semiregular spaces, and weakly H -closed spaces, related to H -closed spaces.

An effective proof of the hyperelliptic Shafarevich conjecture

Rafael von Känel (2014)

Journal de Théorie des Nombres de Bordeaux

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Let C be a hyperelliptic curve of genus g 1 over a number field K with good reduction outside a finite set of places S of K . We prove that C has a Weierstrass model over the ring of integers of K with height effectively bounded only in terms of g , S and K . In particular, we obtain that for any given number field K , finite set of places S of K and integer g 1 one can in principle determine the set of K -isomorphism classes of hyperelliptic curves over K of genus g with good reduction outside...