Iryna Kashuba

Discrete and continuous exponential transforms of simple Lie groups of rank 2

We develop and describe continuous and discrete transforms of class functions on compact simple Lie group G as their expansions into series of uncommon special functions, called here E-functions in recognition of the fact that the functions generalize common exponential functions. The rank of G is the number of variables in the E-functions. A uniform discretization of the decomposition problem is described on lattices of any density and symmetry admissible for the Lie group G.

Graded contractions of Jordan algebras and of their representations

Contractions of Jordan algebras and Jordan superalgebras which preserve a chosen grading are defined and studied. Simultaneous grading of Jordan algebras and their representation spaces is used to develop a theory of grading, preserving contractions of representations of Jordan algebras.

The variety of three-dimensional real Jordan algebras

In this paper, we study the variety

Generalized Loop Modules for Affine Kac–Moody Algebras

Jor_{3}

On E-functions of semisimple Lie groups

of three-dimensional Jordan algebras over the field of real numbers. We establish the list of

Induced Modules for Affine Lie Algebras

26

Structure of parabolically induced modules for affine Kac–Moody algebras

non-isomorphic Jordan algebras and describe the irreducible components of

THE NUMBER OF SYMMETRIC COLORINGS OF THE DIHEDRAL GROUP D-3

Jor_{3}

Derivations of the Lie algebra of infinite strictly upper triangular matrices over a commutative ring

proving that it is the union of Zariski closure of the orbits of

Free Field Realizations of Induced Modules for Affine Lie Algebras

8