This is the first textbook treatment of work leading to the landmark 1979 Kazhdan-Lusztig
Conjecture on characters of simple highest weight modules for a semisimple Lie algebra …

1.1. This work is a natural continuation of [19, 20, 221 which we refer to as I, II, III and whose
notation we adopt. Throughout g is a complex semisimple Lie algebra, ha Cartan …

Furthermore, introduce two superalgebras NS and R as follows (all the necessary
background on Lie superalgebras may be found in [5], Chapter I). Set NSo= Ro= W bh· 1 fd …

1.1. Let g be a semisimple Lie algebra and U (g) its enveloping algebra. A famous theorem
of Kostant ([13];[2], 8.2. 4) asserts that U (g) is a free module over its centre Z (g). More …

This paper provides a unified approach to results on representations of affine Hecke
algebras, cyclotomic Hecke algebras, affine BMW algebras, cyclotomic BMW algebras …

We give a complete combinatorial answer to Kostant's problem for simple highest weight
modules indexed by fully commutative permutations. We also propose a reformulation of …

We give a complete combinatorial classification of those parabolic Verma modules in the
principal block of the parabolic category $\mathcal {O} $ associated to a minimal or a …

We study the classical problem of Kostant for Whittaker modules over Lie algebras and Lie
superalgebras. We give a sufficient condition for a positive answer to Kostant's problem for …

Drinfeld Functor and Finite-Dimensional Representations of Yangian Page 1 Commun. Math.
Phys. 205, 1 – 18 (1999) Communications in Mathematical Physics © Springer-Verlag 1999 …

Abstract A Bernstein-Gelfand-Gelfand resolution for arbitrary Kac-Moody algebras and
arbitrary subsets of the set of simple roots is proven. Moreover, quantum group analogs of …