Linear liftings of skew symmetric tensor fields of type (1, 2) to Weil bundles

The paper contains a classification of linear liftings of skew symmetric tensor fields of type (1, 2) on n-dimensional manifolds to tensor fields of type (1, 2) on Weil bundles under the condition that n ⩾ 3. It complements author’s paper “Linear liftings of symmetric tensor fields of type (1, 2) to Weil bundles” (Ann. Polon. Math. 92, 2007, pp. 13–27), where similar liftings of symmetric tensor fields were studied. We apply this result to generalize that of author’s paper “Affine liftings of torsion-free connections to Weil bundles” (Colloq. Math. 114, 2009, pp. 1–8) and get a classification of affine liftings of all linear connections to Weil bundles.     

The natural operators lifting connections to higher order cotangent bundles

We prove that the problem of finding all Mf _m -natural operators C: Q ? QT ^r * lifting classical linear connections ? on m-manifolds M into classical linear connections C _M (?) on the r-th order cotangent bundle T ^r *M = J ^r (M, ?)₀ of M can be reduced to the well known one of describing all M f _m -natural operators D: Q ? ? ^p T ? ? ^q T* sending classical linear connections ? on m-manifolds M into tensor fields D _M (?) of type (p, q) on M.     

The natural operators lifting 1-forms on manifolds to the bundles ofA-velocities

LetA be a Weil algebra withp variables. We prove that forn-manifolds (np+2) the set of all natural operatorsT ^*T ^* T ^A is a free finitely generated module over a ring canonically dependent onA. We construct explicitly the basis of this module.     

从β0到E(p,q)和E0(p,q)空间的复合算子

设ψ是单位园盘D到自身的解析映射,X是D上解析函数的Banach空间,对f∈X,定义复合算子Cψ:Cψ(f)=foψ.我们利用从β0到E(p,q)和E0(p,q)空间的复合算子研究了空间E(p,q)和E0(p,q),给出了-个新的特征.     

从B~0到E(p，q)和E_0(p，q)空间的复合算子(英文)

设φ是单位园盘D到自身的解析映射,X是D上解析函数的Banach空间,对f∈X,定义复合算子C_φ∶C_φ)(f)=fφ．我们利用从B~0到E(p,q)和E_0(p,q)空间的复合算子研究了空间E(p,q)和E_0(p,q),给出了一个新的特征．     

An algebraic characterization of sets of type (0,n)1 inAG(2,q)

In this paper we prove that inAG(2,q) a set of type (0,n)₁ exists if and only if an algebraic systemS admits solutions inGF(q ²).     

Ensembles de classe (0, 1, q,q + 1) de PG (d,q)

We determine all sets Q of points of any finite dimensional protective space P such that each line intersecting Q in more than one point, either is contained in Q or contains exactly one point not on Q. If P is a finite protective space of order q, these sets are the so called sets of class (0, 1, q, q + 1).     

Hecke operators on Γ0(m)

Ohne Zusammenfassung     

Linear (q+1)-fold Blocking Sets in PG(2, q4)

A (q+1)-fold blocking set of size (q+1)(q⁴+q²+1) in PG(2, q⁴) which is not the union of q+1 disjoint Baer subplanes, is constructed     

Sets of type (M,N) mod q with respect to hyperplanes in PG(r,q)

In this work we study the sets of type (M,N) mod q-with respect to hyperplanes in PG(r,q), where N-M is a coprime of q.     

Degenerate Principal Series Representations of U(p, q) and Spin0(p, q)

Let p>q and let G be the group U(p, q) or Spin₀(p, q). Let P=LN be the maximal parabolic subgroup of G with Levi subgroup where

Induced operators on symmetry classes of tensors

Let be an -dimensional Hilbert space. Suppose is a subgroup of the symmetric group of degree , and is a character of degree 1 on . Consider the symmetrizer on the tensor space

defined by and . The vector space

is a subspace of , called the symmetry class of tensors over associated with and . The elements in of the form are called decomposable tensors and are denoted by . For any linear operator acting on , there is a (unique) induced operator acting on satisfying

In this paper, several basic problems on induced operators are studied.

     

The closed ideal of (c o ,p,q)-summing operators

For 1/p+1/q1, we study the closed ideal formed by the (c _o ,p,q)-summing operators. It turns out thatT:XY does not belong to if and only if it factors the mapId:l _p ^*l _q . By localization, we get the ideal that consists of those operatorsT for which all ultrapowersT ^u are contained in . Operators in the complement of are characterized by the property that they factor the mapsId:l _p ^*n l _q ⁿ uniformly. Our main tools are ideal norms.Supported by DFG grant PI 322/1-2