, Volume 13, Issue 3-4, pp 671-713
Date: 18 Sep 2008

On Rationality of W-algebras

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Abstract

We study the problem of classification of triples ( \( \mathfrak{g} \) ; f; k), where g is a simple Lie algebra, f its nilpotent element and k \( \mathbb{C} \) , for which the simple W-algebra W k ( \( \mathfrak{g} \) ; f) is rational.

Dedicated to Bertram Kostant on the occasion of his 80th birthday
Supported in part by NSF grant DMS-0501395.
Supported in part by Department of Mathematics MIT, Clay Mathematical Institute, grant-in-aid for scientific research A-14204003, and the twenty-first century COE program at RIMS.