In an earlier work, the authors developed a rigged configuration model for the crystal B(∞) (which also descends to a model for irreducible highest weight crystals via a cutting procedure). However, the result obtained was only valid in finite types, affine types, and simply-laced indefinite types. In this paper, we show that the rigged configuration model proposed does indeed hold for all symm...

Demazure’s character formula for arbitrary Kac-Moody Lie algebra was given by S.Kumar and O.Mathieu independently ([6],[8]) by using geometric methods. In 1995, P.Littelmann gave some conjecture (partially solved by himself) about the relation between Demazure’s character formula and crystal bases [7], which was solved affirmatively by M.Kashiwara [3]. Then it gave purely algebraic proof for De...

Communication over channels that may vary in an arbitrary and unknown manner from channel use to channel use is studied. Such channels fall in the framework of arbitrarily varying channels (AVCs), for which it has been shown that the classical deterministic approaches with pre-specified encoder and decoder fail if the AVC is symmetrizable. However, more sophisticated strategies such as common r...

Given a projective variety X and a smooth projective curve C one may consider the moduli space of maps C → X. This space admits certain compactification whose points are called quasi-maps. In the last decade it has been discovered that in the case when X is a (partial) flag variety of a semi-simple algebraic group G (or, more generally, of any symmetrizable Kac-Moody Lie algebra) these compacti...

Matrices are the most common representations of graphs. They are also used for the representation of algebras and cluster algebras. This paper shows some properties of matrices in order to facilitate the understanding and locating symmetrizable matrices with specific characteristics, called positive quasi-Cartan companion matrices. Here, symmetrizable matrix are those which are symmetric when m...