## Description

LiE is the name of a software package that enables mathematicians
and physicists to perform computations of a Lie group theoretic
nature. It focuses on the representation theory of complex
semisimple (reductive) Lie groups and algebras, and on the
structure of their Weyl groups and root systems.
LiE does not compute directly with elements of the Lie groups and
algebras themselves; it rather computes with weights, roots,
characters and similar objects. Some specialities of LiE are:
tensor product decompositions, branching to subgroups, Weyl group
orbits, reduced elements in Weyl groups, distinguished coset
representatives and much more. These operations have been
compiled into the program which results in fast execution:
typically one or two orders of magnitude faster than similar
programs written in a general purpose program.

The LiE programming language makes it possible to customise and
extend the package with more mathematical functions. A user manual
is provided containing many examples.

LiE establishes an interactive environment from which commands
can be given that involve basic programming primitives and
powerful built-in functions. These commands are read by an
interpreter built into the package and passed to the core of the
system. This core consists of programs representing some 100
mathematical functions. The interpreter offers on-line facilities
which explain operations and functions, and which give background
information about Lie group theoretical concepts and about
currently valid definitions and values.

A more extensive description of LiE is availble as a dvi file.