<p>This book collects important results concerning the classification and properties of nilpotent orbits in a Lie algebra. It develops the Dynkin-Kostant and Bala-Carter classifications of complex nilpotent orbits and derives the Lusztig-Spaltenstein theory of induction of nilpotent orbits.</p>

Nilpotent Orbits In Semisimple Lie Algebra: An Introduction

Science & Math

McGovern, William M.

Collingwood, David H.

Mathematics

Chapman and Hall/CRC

Representations of Rank One Lie Groups II: N-Cohomology (Memoirs of the American Mathematical Society)

Amer Mathematical Society

This book investigates the composition series of generalized  principal series representations induced from a maximal cuspidal  parabolic subgroup of a real reductive Lie group. Boe and  Collingwood study when such representations are  multiplicity-free (Vogan's Problem #3) and the problem of  describing their composition factors in closed form. The results  obtained are strikingly similar to those of Enright and Shelton  for highest weight modules. Connections with two different flag  variety decompositions are discussed.

Enright-Shelton Theory and Vogan's Problem for Generalized Principal Series (Memoirs of the American Mathematical Society)

Boe, Brian D.

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