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1.
We consider two combinatorial statistics on permutations. One is the genus. The other, , is defined for alternating permutations, as the sum of the number of descents in the subwords formed by the peaks and the valleys. We investigate the distribution of on genus zero permutations and Baxter permutations. Our q-enumerative results relate the statistic to lattice path enumeration, the rank generating function and characteristic polynomial of noncrossing partition lattices, and polytopes obtained as face-figures of the associahedron.  相似文献   

2.
Let be the affine Lie algebra associated to the simple finite-dimensional Lie algebra . We consider the tensor product of the loop -module associated to the irreducible finite-dimensional -module V() and the irreducible highest weight -module L k,. Then L k, can be viewed as an irreducible module for the vertex operator algebra M k,0. Let A(L k,) be the corresponding -bimodule. We prove that if the -module is zero, then the -module is irreducible. As an example, we apply this result on integrable representations for affine Lie algebras.  相似文献   

3.
Oriented special spines of 3-manifolds are studied. (Orientation is an additional structure on the spine, and each 3-manifold possesses a special spine with such a structure.) The transformations (moves) and of special spines, which do not change the manifold, are well known. It is proved that and preserve orientability of a spine, while and do not. For spines of homology balls, a class of moves is described allowing one to pass from a given orientation of a spine to any other orientation of the spine. Bibliography: 6 titles.  相似文献   

4.
We give a construction of the left adjoint of the comparison functor in one step and we give a characterization of separated (finitely) positively convex spaces.  相似文献   

5.
Let be a Kac–Moody algebra, U(x,y) be a function defined in , and a be a constant element of . We prove that the equation U xy = [[U,a],U x] has two symmetry hierarchies connected by a gauge transformation. In particular, the well-known Konno equation appears in the case of the algebra . The corresponding symmetry hierarchies contain the nonlinear Schrödinger and the Heisenberg magnet equations.  相似文献   

6.
A bi-Lipschitz continuous mapping of a space X is a bijection such that , where . We write if f is a Lipschitz (bi-Lipschitz) mapping of X into itself and denote by the set of all bi-Lipschitz mappings of X that are not isometry. Thus, if and blip . For X we consider a standard Cantor set K on the real line (with standard metric). The main result of this paper is formulated as follows: where Bibliography: 2 titles.  相似文献   

7.
Let be the rational function field with finite constant field and characteristic , and let K/k be a finite separable extension. For a fixed place v of k and an elliptic curve E/K which has ordinary reduction at all places of K extending v, we consider a canonical height pairing which is symmetric, bilinear and Galois equivariant. The pairing for the infinite place of k is a natural extension of the classical Néron–Tate height. For v finite, the pairing plays the role of global analytic p-adic heights. We further determine some hypotheses for the nondegeneracy of these pairings.  相似文献   

8.
A class of centrally-symmetric convex 12-topes (12-hedrons) in is described such that for an arbitrary prescribed norm on each polyhedron in the class can be inscribed in (circumscribed about) the -ball via an affine transformation, and this can be done with large degree of freedom. Bibliography: 5 titles.  相似文献   

9.
The C *-algebra generated by the operators of pseudodifferential boundary value problems on a manifold with smooth closed disjoint edges and boundary is studied. The operators act in the space L 2( ) L 2( ). The goal of this paper is to describe all (up to an equivalence) irreducible representations of the algebra Bibliography: 12 titles.  相似文献   

10.
Let be an Abelian unital C *-algebra and let denote its Gelfand spectrum. We give some necessary and sufficient conditions for a nondegenerate representation of to be unitarily equivalent to a representation in which the elements of act multiplicatively, by their Gelfand transforms, on a space L 2( ,), where is a positive measure on the Baire sets of . We also compare these conditions with the multiplicity-free property of a representation.  相似文献   

11.
We consider motivic category of pairs (smooth projective scheme, separable algebra) over a given field. For any separable extension L/Fwe construct the Weil transfer functor . This enables us to compute K-groups of schemes obtained by means of Weil restriction.  相似文献   

12.
Starting from the commutation relations in a complex semisimple Lie algebra , one may obtain a space of vector fields on Euclidean space such that and are isomorphic when is equipped with the usual Lie bracket between vector fields and the isotropy subalgebra of is a Borel subalgebra . Furthermore, one may adjoin to the vector fields in multiplication operators to obtain an -parameter family of distinct presentations of as spaces of differential operators, where is the dual of a Cartan subalgebra. Some of these presentations will preserve a space of polynomials on Euclidean space, and, in fact, all the finite-dimensional representations of can be presented in this way. All of this is carried out explicitly for arbitrary . In doing so, one discovers there is a Lie group of diffeomorphisms of the unipotent subgroup N complementary to B which acts on these presentations and preserves a certain notion of weight.  相似文献   

13.
The rigid isotopy classification of nonsingular real algebraic curves of bidegree on the Hirzebruch surface (the projective plane with a point blown up) is obtained. Consequences for the space of curves with a single node or a cusp on a hyperboloid and on are given. Bibliography: 15 titles.  相似文献   

14.
The sequence of orthogonal polynomials is said to be classical if is also orthogonal. The aim of this paper is to find the sequences which have the property that is also orthogonal. We prove that sequences, with this property have to be, classical and belong either to the set of Laguerre or Jacobi polynomials, where in the Laguerre case c has to be zero and in the Jacobi case c = ±1.  相似文献   

15.
The 3-local geometry of the sporadic simple group Co1 has been known to have a cover with a flag-transitive automorphism group which is a nonsplit extension of an elementary Abelian 2-group of rank 24 (the Leech lattice modulo 2) by Co1. It was conjectured that was simply connected. We disprove this conjecture by constructing a double cover of . The automorphism group of is of the shape . However, it is not isomorphic to the involution centralizer of the Monster sporadic simple group.  相似文献   

16.
Dedicated to Professor Jacque-Louis Lions on the occasion of his 70th birthday We consider a mixed problem for the operator
in a noncylindrical domain . We obtain local solution in t. When we add a viscosity we obtain a global solution. We also investigate the asymptotic behavior of the energy.  相似文献   

17.
In this paper we prove that there are no self-extensions of simple modules over restricted Lie algebras of Cartan type. The proof given by Andersen for classical Lie algebras not only uses the representation theory of the Lie algebra, but also representations of the corresponding reductive algebraic group. The proof presented in the paper follows in the same spirit by using the construction of a infinite-dimensional Hopf algebra D(G) u( ) containing u( ) as a normal Hopf subalgebra, and the representation theory of this algebra developed in our previous work. Finite-dimensional hyperalgebra analogs D(G r ) u( ) have also been constructed, and the results are stated in this setting.  相似文献   

18.
Book Notices   总被引:1,自引:0,他引:1  
Given the minimization problem of a real-valued function let A be any algorithm of type with that converges to a local minimum . In this note, new assumptions on f(x) under which A converges linearly to x* are established. These include the ones introduced in the literature which involve the uniform convexity of f(x).  相似文献   

19.
We propose new formulas for singular vectors in Verma modules over the affine Lie superalgebra . We analyze the coexistence of singular vectors of different types and identify the twisted modules arising as submodules and quotient modules of Verma modules. We show that with the twists (spectral flow transformations) properly taken into account, a resolution of irreducible representations can be constructed consisting of only the modules.  相似文献   

20.
Two results on composed functions are proven. First we give conditions on and so that the mean behaves like , if , including the examples
1$$ " align="middle" border="0"> , not an integer for . Secondly we find conditions on the real positive numbers , such that are almost periodic and we compute their mean values and spectra.  相似文献   

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