DEGREE CONES AND MONOMIAL BASES OF LIE ALGEBRAS AND QUANTUM GROUPS

Monomial Relization of Crystal Bases for Special Linear Lie Algebras

We give a new realization of crystal bases for finite dimensional irreducible modules over special linear Lie algebras using the monomials introduced by H. Nakajima. We also discuss the connection between this monomial realization and the tableau realization given by Kashiwara and Nakashima. Introduction The quantum groups, which are certain deformations of the universal enveloping algebras of ...

Bases in Lie and Quantum Algebras

Applications of algebras in physics are related to the connection of measurable observables to relevant elements of the algebras, usually the generators. However, in the determination of the generators in Lie algebras there is place for some arbitrary conventions. The situation is much more involved in the context of quantum algebras, where inside the quantum universal enveloping algebra, we ha...

Quantum Algebras and Lie Groups A

Quantum groups are born in Leningrad[1] in connection with the quantum inverse problem method as it arises in soliton theory. Other motivations came out after and the logic of the subject has been repeatedly reversed[2] and it is still not univocally established. The approach followed here attempts to use the link of the field with Lie groups as much as it is possible at the moment and, perhaps...

Lie Groups and Lie Algebras

Lie Groups and Lie Algebras

A Lie group is, roughly speaking, an analytic manifold with a group structure such that the group operations are analytic. Lie groups arise in a natural way as transformation groups of geometric objects. For example, the group of all affine transformations of a connected manifold with an affine connection and the group of all isometries of a pseudo-Riemannian manifold are known to be Lie groups...