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Spherical Unitary dual for quasisplit real groups
quasisplit real groups Spherical Unitary
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2015/8/17
G is the real points of a linear connected reductive group.
- g0 := Lie(G), Cartan involution, g0 = k0 + s0, g := (g0)C, K
maximal compact subgroup, g = k + s,
- P = MAN minimal parabolic subgrou...
SPHERICAL UNITARY DUAL FOR COMPLEX CLASSICAL GROUPS
CLASSICAL GROUPS SPHERICAL UNITARY DUAL
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2015/8/17
The full unitary dual for the complex classical groups viewed as real Lie
groups is computed in [B1]. This was close to 20 years ago. Since then there
have been many advances, but the general proble...
SPHERICAL UNITARY REPRESENTATIONS FOR SPLIT REAL AND P-ADIC GROUPS
UNITARY REPRESENTATIONS P-ADIC GROUPS
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2015/8/17
1.1. Positive de nite functions. We start with the classical notion of
positive de nite functions.
De nition. A continuous function f : R ! C is called positive de nite if
it satis es
(1...
Sub-Geometries of Lie Sphere Differential Geometry
Sub-Geometries Lie Sphere Differential Geometry
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2015/3/24
Sub-Geometries of Lie Sphere Differential Geometry.
The planar circular restricted three body problem in the lunar case
The planar circular restricted three body problem lunar case
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2015/3/18
The course is a short introduction to some aspects of the simplest non-integrable three body problem, the study of which goes back to the seminal works of Hill, Poincar′e and Birkhoff. After Goursat (...
On the sums of two cubes
sums two cubes
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2011/2/28
We solve the equation f(x, y)3 + g(x, y)3 = x3 + y3 for homogeneous f, g ∈ C(x, y), completing an investigation begun by Vi`ete in 1591. The usual addition law for elliptic curves and composition give...
Schurity of S-rings over a cyclic group and generalized wreath product of permutation groups
Schurity of S-rings cyclic group generalized wreath product of permutation groups
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2011/2/25
The generalized wreath product of permutation groups is intro-duced. By means of it we study the schurity problem for S-rings over a cyclic group G and the automorphism groups of them.
Disordered, Quasicrystalline and Crystalline Phases of Densely Packed Tetrahedra
Disordered Quasicrystalline Crystalline Phases Densely Packed Tetrahedra
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2011/3/3
Noncommutative field theories are a class of theories beyond the standard model of elementary particle physics. Their importance may be summarized in two facts.Firstly as field theories on noncommutat...
The bounded spherical functions for the free two step nilpotent Lie group
nilpotent Lie group representation theory spherical function
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2011/1/19
In this paper, we give the expressions for the bounded spherical functions, or equivalently the spherical functions of positive type, for the free two-step nilpotent Lie groups endowed with the action...
Exceptional collections on toric Fano threefolds and birational geometry
Exceptional collections toric Fano threefolds birational geometry
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2011/2/22
Bernardi and Tirabassi show the existence of a full strong excep-tional collection consisting of line bundles on smooth toric Fano 3-folds under assuming Bondal’s conjecture, which states that the Fro...
Circular planar nearrings: geometrical and combinatorial aspects
Planar nearring BIBD Circular Disk Field
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2011/1/18
Let (N, Φ) be a circular Ferrero pair. We define the disk with center b and radius a, D(a; b), as D(a; b) = {x ∈ Φ(r) +c | r 6= 0, b ∈ Φ(r) +c, |(Φ(r) +c) ∩ (Φ(a)+b)| = 1}.We prove that in the field-g...
The number of convex pentagons and hexagons in an $n$-triangular net
n-triangular net convex pentagon convex hexagon regular hexagon
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2011/2/22
In this paper, we obtain the counting formulaes of convex pentagons and convex hexagons, respectively, in an n-triangular net by solving the corresponding recursive formulaes.
Effective Action and Phase Transitions in Thermal Yang-Mills Theory on Spheres
Confinement Nonperturbative Effects QCD
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2011/3/2
We study the covariantly constant Savvidy-type chromomagnetic vacuum in finite-temperature
Yang-Mills theory on the four-dimensional curved spacetime. Motivated by the fact that a positive spatial cu...
Petrov-Galerkin Finite Volumes
Finite volumes mixed finite elements Petrov-Galerkin variational formulation
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2011/1/19
For an elliptic problem with two space dimensions, we propose to formulate the finite volume method with the help of Petrov-Galerkin mixed finite elementsthat are based on the building of a dual Ravia...
Fourth order curvature flows and geometric applications
Fourth order curvature flows geometric applications
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2011/1/17
We study a class of fourth order curvature flows on a compact Riemannian manifold, which
includes the gradient flows of a number of quadratic geometric functionals, as for instance the
L2 norm of th...