Multi-graded nilpotent tuples

A Pseudo-differential Calculus on Graded Nilpotent Lie Groups

In this paper, we present first results of our investigation regarding symbolic pseudo-differential calculi on nilpotent Lie groups. On any graded Lie group, we define classes of symbols using difference operators. The operators are obtained from these symbols via the natural quantisation given by the representation theory. They form an algebra of operators which shares many properties with the...

A Nilpotent Quotient Algorithm for Graded Lie Rings

A nilpotent quotient algorithm for graded Lie rings of prime characteristic is described. The algorithm has been implemented and applications have been made to the investigation of the associated Lie rings of Burnside groups. New results about Lie rings and Burnside groups are presented. These include detailed information on groups of exponent 5 and 7 and their associated Lie rings. Appeared: J...

Graded Characters of Modules Supported in the Closure of a Nilpotent Conjugacy Class

This is a combinatorial study of the Poincaré polynomials of isotypic components of a natural family of graded GL(n)-modules supported in the closure of a nilpotent conjugacy class. These polynomials generalize the Kostka-Foulkes polynomials and are q-analogues of Littlewood-Richardson coefficients. The coefficients of two-column Macdonald-Kostka polynomials also occur as a special case. It is ...

Interval prediction for graded multi-label classification

Performance Measures for Multi-Graded Relevance

We extend performance measures commonly used in semantic web applications to be capable of handling multi-graded relevance data. Most of today's recommender social web applications o er the possibility to rate objects with di erent levels of relevance. Nevertheless most performance measures in Information Retrieval and recommender systems are based on the assumption that retrieved objects (e. g...