in this paper we describe how the degrees of the irreducible characters of the affine subgroups of the classical groups under consideration can be found inductively. in [4] gow obtained certain character degrees for all of the affine subgroups of the classical groups. we apply the method of fischer to the above groups and, in addition to the character degrees given in [4], we obtain some new ch...

In this paper, we first introduce the notion of $c$-affine functions for $c> 0$. Then we deal with some properties of strongly convex functions in real inner product spaces by using a quadratic support function at each point which is $c$-affine. Moreover, a Hyers–-Ulam stability result for strongly convex functions is shown.

We study the property of a normal scheme, that the complement of every hypersurface is an affine scheme. To this end we introduce the affine class group. It is a factor group of the divisor class group and measures the deviation from this property. We study the behaviour of the affine class group under faithfully flat extensions and under the formation of products, and we compute it for differe...

‎highest weight modules of the double affine lie algebra $widehat{widehat{mathfrak{sl}}}_{2}$ are studied under a‎ ‎new triangular decomposition‎. ‎singular vectors of verma modules are‎ ‎determined using a similar condition with horizontal affine lie‎ ‎subalgebras‎, ‎and highest weight modules are described under the‎ ‎condition $c_1>0$ and $c_2=0$.

We give a self–contained introduction into the metric–affine gauge theory of gravity. Starting from the equivalence of reference frames, the prototype of a gauge theory is presented and illustrated by the example of Yang–Mills theory. Along the same lines we perform a gauging of the affine group and establish the geometry of metric–affine gravity. The results are put into the dynamical framewor...

It is well-known that affine equivalence relations keep nonlineaerity invariant for all Boolean functions. The set of all Boolean functions, Fn, over IF n 2 , is naturally regarded as the 2 n dimensional vector space, IF n 2 . Thus, while analyzing the transformations acting on Fn, S22n , the group of all bijective mappings, defined from IF 2 2 onto itself should be considered. As it is shown i...

Let G be a connected reductive algebraic group. We prove that for quasi-affine G-spherical variety the weight monoid is determined by weights of its non-trivial ???? -actions are homogeneous with respect to Borel subgroup G. As an application we get smooth affine spherical non-isomorphic torus automorphism group (considered as ind-group) inside category irreducible varieties.

A simple replacement approach is used to construct new symmetric and affine designs from projective or affine spaces. This is used to construct symmetric designs with a given automorphism group, to study GMW-designs, and to construct new affine designs whose automorphism group fixes a point and has just two pointand block-orbits.

Let G be a reductive algebraic group and H a closed subgroup of G. An affine embedding of the homogeneous space G/H is an affine G-variety with an open G-orbit isomorphic to G/H . The homogeneous space G/H admits an affine embedding if and only if G/H is a quasi-affine algebraic variety. We start with some basic properties of affine embeddings and consider the cases, where the theory is well-de...

In this paper, we propose a 2-parameter family of coupled Painlevé II systems in dimension four with affine Weyl group symmetry of type D (2) 3. We also propose a 4-parameter family of 2-coupled D (2) 3-systems in dimension eight with affine Weyl group symmetry of type D In this paper, we present a 2-parameter family of 2-coupled Painlevé II systems with affine Weyl group symmetry of type D