Normalized irreducible characters of the symmetric group S(n) can be understood as zonal spherical functions of the Gelfand pair (S(n)×S(n),diag S(n)). They form an orthogonal basis in the space of the functions on the group S(n) invariant with respect to conjugations by S(n). In this paper we consider a different Gelfand pair connected with the symmetric group, that is an “unbalanced” Gelfand ...

The purpose of this study was to examine the relationship between intellectual ability, Cooperative type think pair share learning model, and Entrepreneur lesson in grade ten at a vocational high school Sungai Penuh. This is Quasi-experiment nature. Purposeful sampling used study. In total, 103 students made up study's sample. We two instruments obtain data: an experimental one validated one. h...

We review some basic facts on vector fields, in the complex- analytic setting, thus obtaining a rationality result and an extension of Birkhoff–Grothendieck theorem, as follows: Let $Z$ be compact complex manifold endowed with very ample line bundle $L$ . Denote by $\mathfrak {g}_L$ extended Lie algebra infinitesimal automorphisms If representation space holomorphic sections is irreducible th...

Let $\Gamma$ be an irreducible lattice in a product of two locally compact groups and assume that is densely embedded profinite group $K$. We give necessary conditions which imply the left translation action $\Gamma \curvearrowright K$ “virtually” cocycle superrigid: any ${w\colon \Gamma\times K\rightarrow\Delta}$ with values countable $\Delta$ cohomologous to factors through map $\Gamma\times ...

Let G = 〈A,B〉 be a non-elementary two generator subgroup of Isom(H). If G is discrete and free and geometrically finite, its quotient is a pair of pants and in [5] we produced a formula for the number of essential self intersections (ESIs) of any primitive geodesic on the quotient. An ESI is a point where the geodesic has a self-intersection on a seam. Self-intersections of geodesics on arbitra...

Using an invariant of Cuntz, we classify reducible shifts of nite type with two irre-ducible components up to ow equivalence. 0. Introduction Let A be an n n matrix over the non-negative integers Z +. Form a directed graph G A with n vertices and A(i; j) edges from vertex i to vertex j. Let E be the set of all edges of G A endowed with the discrete topology. Then the product space E Z is a comp...

In class, we’ve been talking about the integers, which we’ve denoted Z. We started off talking about equality in Z, but then moved on to talking about congruences, which is a weaker notion. This handout explains how “congruence modulo n” is something called an equivalence relation, and we can use it to construct a set Z/nZ that’s a “quotient” of Z. The key point is that a congruence modulo n in...

Flaminio and Montagna (2008) enlarged the language of MV-algebras by a unary operation σ, called internal state or a state operator, equationally defined so as to preserve the basic properties of a state in its usual meaning. The resulting class of MV-algebras is called state MV-algebras. Jenča (2007) and Vetterlein (2008), using different approaches, represented MV-algebras through the quotien...

Let M be a compact connected Fujiki manifold, G semisimple affine algebraic group over C with one simple factor and P fixed proper parabolic subgroup of G. For holomorphic principal G–bundle EG M, let EP the P–bundle EG⟶EG/P given by quotient map. We prove that following three statements are equivalent: (1) ad(EG) is numerically flat, (2) line bundle ⋀topad(EP)⁎ nef, (3) for every reduced irred...