In this paper, using generating functions we study two categories E and C of modules for twisted affine Lie algebras ĝ[σ], which were firstly introduced and studied in [Li] for untwisted affine Lie algebras. We classify integrable irreducible ĝ[σ]-modules in categories E and C, where E is proved to contain the well known evaluation modules and C to unify highest weight modules, evaluation modul...

A b s t r a c t . In this contribution we consider the stability of linearity and differential uniformity of vector Boolean functions under certain constructions and modifications. These include compositions with affine surjections onto the input space and with aitlne surjections from the output space, inversions, adding coordinate functions, forming direct sums and restrictions to affine subsp...

We introduce the affine ensemble, a class of determinantal point processes (DPP) in half-plane $\mathbb{C}^{+}$ associated with $ax + b$ (affine) group, depending on an admissible Hardy function $\psi$. obtain asymptotic behavior variance, exact value constant, and non-asymptotic upper lower bounds for variance compact set $\Omega \subset \mathbb{C}^{+}$. As special case one recovers DPP relate...

Let G be a compact definable C group, X a compact affine definable CG manifold and 2 ≤ r < ∞. We prove that the set of equivariant definable Morse functions on X whose loci are finite unions of nondegenerate critical orbits is open and dense in the set of G invariant definable C functions with respect to the definable C topology.

In [13] for a given vectorial Boolean function F from F2 to itself it was defined an associated Boolean function γF (a, b) in 2n variables that takes value 1 iff a 6= 0 and equation F (x) + F (x + a) = b has solutions. In this paper we introduce the notion of differentially equivalent functions as vectorial functions that have equal associated Boolean functions. It is an interesting open proble...

We define a new family F̃w(X) of generating functions for w ∈ S̃n which are affine analogues of Stanley symmetric functions. We establish basic properties of these functions such as their symmetry and conjecture certain positivity properties. As an application, we relate these functions to the k-Schur functions of Lapointe, Lascoux and Morse as well as the cylindric Schur functions of Postnikov. ...