دانلود کتاب Invariant Differential Operators. Noncompact Semisimple Lie Algebras and Groups

Invariant differential operators play a very important role in the description of
physical symmetries – recall, e.g., the examples of Dirac, Maxwell, Klein–Gordon,
d’Almbert, and Schrödinger equations. Invariant differential operators played and
continue to play important role in applications to conformal field theory. Invariant
superdifferential operators were crucial in the derivation of the classification of positive
energy unitary irreducible representations of extended conformal supersymmetry
first in four dimensions, then in various dimensions. Last, but not least, among our
motivations are the mathematical developments in the last 50 years and counting.
Obviously, it is important for the applications in physics to study these operators
systematically. A few years ago we have given a canonical procedure for the construction
of invariant differential operators. Lately, we have given an explicit description
of the building blocks, namely, the parabolic subgroups and subalgebras from which
the necessary representations are induced.
Altogether, over the years we have amassed considerable material which was
suitable to be exposed systematically in book form. To achieve portable formats, we
decided to split the book in two volumes. In the present first volume, our aim is to
introduce and explain our canonical procedure for the construction of invariant differential
operators and to explain how they are used on many series of examples.
Our objects are noncompact semisimple Lie algebras, and we study in detail a family
of those that we call “conformal Lie algebras” since they have properties similar
to the classical conformal algebras of Minkowski space-time. Furthermore, we extend
our considerations to simple Lie algebras that are called “parabolically related” to the
initial family.
The second volume will cover various generalizations of our objects, e.g.,
the AdS/CFT correspondence, quantum groups, superalgebras, infinite-dimensional
(super-)algebras including (super-)Virasoro algebras, and (q-)Schrödinger algebras