Kostka-Foulkes polynomials for symmetrizable Kac-Moody algebras

We introduce a generalization of the classical Hall-Littlewood and Kostka-Foulkes polynomials to all symmetrizable Kac-Moody algebras. We prove that these Kostka-Foulkes polynomials coincide with the natural generalization of Lusztig's $t$-analog of weight multiplicities, thereby extending a theorem of Kato. For $g$ an affine Kac-Moody algebra, we define $t$-analogs of string functions and use Cherednik's constant term identities to derive explicit product expressions for them.Comment: 19 page

Poincare series of subsets of affine Weyl groups

In this note, we identify a natural class of subsets of affine Weyl groups whose Poincare series are rational functions. This class includes the sets of minimal coset representatives of reflection subgroups. As an application, we construct a generalization of the classical length-descent generating function, and prove its rationality.Comment: 7 page

On growth types of quotients of Coxeter groups by parabolic subgroups

The principal objects studied in this note are Coxeter groups $W$ that are neither finite nor affine. A well known result of de la Harpe asserts that such groups have exponential growth. We consider quotients of $W$ by its parabolic subgroups and by a certain class of reflection subgroups. We show that these quotients have exponential growth as well. To achieve this, we use a theorem of Dyer to construct a reflection subgroup of $W$ that is isomorphic to the universal Coxeter group on three generators. The results are all proved under the restriction that the Coxeter diagram of $W$ is simply laced, and some remarks made on how this restriction may be relaxed.Comment: 10 pages; The exposition has been made more concise and an additional proposition is proved in the final sectio

Industrial Megaprojects: Concepts, strategies and practices for success

This is a review of a recent book on Megaprojects written by an experienced practitioner and researcher of megaprojects who has been writing about them over the last three decades. It focuses on industrial megaprojects covering mainly megaprojects in the Oil & Gas Production, Petroleum Processing and Refining, Minerals and Metals, Chemical, LNG, Power Generation and Pipelines. The book is written mainly from the perspective of project owners but contains some good advice to project managers as well.

K theory of smooth complete toric varieties and related spaces

The K-rings of non-singular complex pro jective varieties as well as quasi- toric manifolds were described in terms of generators and relations in an earlier work of the author with V. Uma. In this paper we obtain a similar description for complete non-singular toric varieties. Indeed, our approach enables us to obtain such a description for the more general class of torus manifolds with locally standard torus action and orbit space a homology polytope.Comment: 11 pages, no figure