Refined geometric realization of a quantum group and Lusztig’s symmetries

ABSTRACT

In this paper, we shall give a refinement of the geometric realization of Lusztig’s algebra f given by Lusztig. This realization gives a geometric interpretation of the decomposition of f. As an application, we shall give geometric realizations of Lusztig’s symmetries on the whole quantum group.

KEYWORDS:

• Drinfeld double
• Geometric realizations
• Lusztig’s algebras
• Lusztig’s symmetries

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 16G20
• 17B37